Dear All,
Please solve it. First of all, this equation was solved by the great mathematician Ramanujan.
1. Solve this equation:
√X + Y = 7
X + √Y = 11
This equation is very interesting. Please try to solve it mathematically. 🤔
With Warm Regards,
Nishi Kant
From India, Jharsuguda
Acknowledge(0)
Amend(0)
Please solve it. First of all, this equation was solved by the great mathematician Ramanujan.
1. Solve this equation:
√X + Y = 7
X + √Y = 11
This equation is very interesting. Please try to solve it mathematically. 🤔
With Warm Regards,
Nishi Kant
From India, Jharsuguda
Acknowledge(0)Amend(0)
Answer is X=9 and y=4 but solve it mathemaically.I mean what is the process... Cool Nishi
From India, Jharsuguda
Acknowledge(0)Amend(0)
From India, Jharsuguda
Acknowledge(0)Amend(0)
Yar, it's again mathematically. In the first equation, if we put numbers only 9 for x and 4 for y, and the same in the second equation. Yar, I know there might be other ways to solve the equation, but in competition, you need to solve problems quickly.
From India
Acknowledge(0)Amend(0)
1From India
Acknowledge(0)Amend(0)
Hi Gent,
I know the value of X and Y in this equation. But I want the mathematical proof. Please note that first of all, this equation was mathematically solved by the great mathematician Ramanujan after regular work of 17 days on the same equation.
Cheers, Nishi Kant
From India, Jharsuguda
Acknowledge(0)Amend(0)
I know the value of X and Y in this equation. But I want the mathematical proof. Please note that first of all, this equation was mathematically solved by the great mathematician Ramanujan after regular work of 17 days on the same equation.
Cheers, Nishi Kant
From India, Jharsuguda
Acknowledge(0)Amend(0)
One of my collegues Ms. Varalakshmi has solved the equation. Find your answer below
Let: .u = √x . → . x = u²
. - - . . . . ._
Let: .v = √y . → . y = v²
Substitute: . u + v² .= . 7 -[1]
. . . . . . . . . u² + v .= .11 .[2]
From [1], we have: .u .= .7 - v²
Substitute into [2]: . (7 - v²)² + v .= .11
. . which simplifies to: .v^4 - 14v² + v + 38 .= .0
. . which factors: .(v - 2)(v³ + 2v² - 10v - 19) .= .0
. . and has the rational root: .v = 2
Substitute into [1]: . u + 2² .= .7 . → . u = 3
Therefore: .x = u² = 9, . y = v² = 4
From India, Hyderabad
Acknowledge(1)
Amend(0)
Let: .u = √x . → . x = u²
. - - . . . . ._
Let: .v = √y . → . y = v²
Substitute: . u + v² .= . 7 -[1]
. . . . . . . . . u² + v .= .11 .[2]
From [1], we have: .u .= .7 - v²
Substitute into [2]: . (7 - v²)² + v .= .11
. . which simplifies to: .v^4 - 14v² + v + 38 .= .0
. . which factors: .(v - 2)(v³ + 2v² - 10v - 19) .= .0
. . and has the rational root: .v = 2
Substitute into [1]: . u + 2² .= .7 . → . u = 3
Therefore: .x = u² = 9, . y = v² = 4
From India, Hyderabad
Acknowledge(1)Amend(0)
My solution: 🧐🔗🔗🔗🔗
I just received the question and attempted to solve it. I obtained two real values of x, two imaginary values of x, and four real values of y. I only considered the real values.
Thank you
Acknowledge(0)Amend(0)
I just received the question and attempted to solve it. I obtained two real values of x, two imaginary values of x, and four real values of y. I only considered the real values.
Thank you
Acknowledge(0)Amend(0)
Let:
Equation Setup
Let:
\[ x = \tan^2 \theta \]
\[ y = \sec^2 \theta \]
1) \(\tan \theta + \sec^2 \theta = 7\)
2) \(\tan^2 \theta + \sec \theta = 11\)
Solving Equation 1
Take 1):
\[ \tan \theta + \frac{1}{\cos^2 \theta} = 7 \]
Solve it, and you will get:
\[ 7\sin^2 \theta + \sin \theta - 6 = 0 \quad (A) \]
Solving Equation 2
Now, similarly, take equation (2) and solve it.
You will get:
\[ 12\cos^2 \theta - \cos \theta - 1 = 0 \quad (B) \]
Solving Equation A
Taking equation (A):
Let:
\[ \sin \theta = t \]
\[ 7t^2 + t - 6 = 0 \]
Solve it, and you will get:
\[ t = -1 \text{ or } t = \frac{6}{7} \]
\[ \sin \theta = -1 \text{ or } \sin \theta = \frac{6}{7} \]
Solving Equation B
Now, take equation (B) and do similarly as equation A:
\[ 12\cos^2 \theta - \cos \theta - 1 = 0 \]
Solve it as above:
\[ \cos \theta = \frac{1}{3} \text{ or } \cos \theta = -\frac{1}{4} \]
Since the cosine value exists in the 3rd quadrant, not negative, \(-\frac{1}{4}\) is not possible. Therefore:
\[ \cos \theta = \frac{1}{3} \]
The sine value exists in the 3rd quadrant, not positive, so:
\[ \sin \theta = -1 \]
Final Calculation
Now,
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} = -1/\frac{1}{3} = -3 \]
\[ x = \tan^2 \theta = (-3)^2 = 9 \]
Put in equation 1:
\[ y = 4 \]
Therefore:
\[ x = 9 \text{ and } y = 4 \text{ is the answer.} \]
From undefined, undefined
Acknowledge(0)Amend(0)
Equation Setup
Let:
\[ x = \tan^2 \theta \]
\[ y = \sec^2 \theta \]
1) \(\tan \theta + \sec^2 \theta = 7\)
2) \(\tan^2 \theta + \sec \theta = 11\)
Solving Equation 1
Take 1):
\[ \tan \theta + \frac{1}{\cos^2 \theta} = 7 \]
Solve it, and you will get:
\[ 7\sin^2 \theta + \sin \theta - 6 = 0 \quad (A) \]
Solving Equation 2
Now, similarly, take equation (2) and solve it.
You will get:
\[ 12\cos^2 \theta - \cos \theta - 1 = 0 \quad (B) \]
Solving Equation A
Taking equation (A):
Let:
\[ \sin \theta = t \]
\[ 7t^2 + t - 6 = 0 \]
Solve it, and you will get:
\[ t = -1 \text{ or } t = \frac{6}{7} \]
\[ \sin \theta = -1 \text{ or } \sin \theta = \frac{6}{7} \]
Solving Equation B
Now, take equation (B) and do similarly as equation A:
\[ 12\cos^2 \theta - \cos \theta - 1 = 0 \]
Solve it as above:
\[ \cos \theta = \frac{1}{3} \text{ or } \cos \theta = -\frac{1}{4} \]
Since the cosine value exists in the 3rd quadrant, not negative, \(-\frac{1}{4}\) is not possible. Therefore:
\[ \cos \theta = \frac{1}{3} \]
The sine value exists in the 3rd quadrant, not positive, so:
\[ \sin \theta = -1 \]
Final Calculation
Now,
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} = -1/\frac{1}{3} = -3 \]
\[ x = \tan^2 \theta = (-3)^2 = 9 \]
Put in equation 1:
\[ y = 4 \]
Therefore:
\[ x = 9 \text{ and } y = 4 \text{ is the answer.} \]
From undefined, undefined
Acknowledge(0)Amend(0)CiteHR is an AI-augmented HR knowledge and collaboration platform, enabling HR professionals to solve real-world challenges, validate decisions, and stay ahead through collective intelligence and machine-enhanced guidance. Join Our Platform.
Security Amount Proof.docx
Grandma proof-Lenovo.zi p