Latest Self Aptitude Question SOLUTION: please slove it as early as possible x^1/2 + y = 7 x + y^1/2 = 11 prove that x = 9 and y = 4

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(#M40037963) SELF question Keep an EYE

please slove it as early as possible
x^1/2 + y = 7
x + y^1/2 = 11

prove that x = 9 and y = 4

Akanksha Mishra (9 years ago)

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Tark Patel  (9 years ago)

Let x^(1/2) = a and y^(1/2) = b
Therefore, a + b² = 7 ---------- (1)
a² + b = 11 ---------- (2)

Multiply (1) by a² and Multiply (2) by a,

a³ + a²b² = 7a² ---------- (1)
a³ + ab = 11a ---------- (2)
Subtract (1) and (2),

a²b² – ab = 7a² – 11a
-> ab(ab – 1) = a(7a – 11)
-> b(ab – 1) = (7a – 11)
-> ab² – b = 7a – 11
-> – b = 7a – ab² – 11
-> – b = a(7 – b²) – 11
a = (11 – b)/(7 – b²)

Let b = 1, 2,3,4 ...
when b = 2
a = (11 – b)/(7 – b²)
= (11 – 2)/(7 – 4) = 9/3 = 3

so a = 3 and b = 2 -> x^(1/2) = 3 and y^(1/2) = 2
Hence x = 9 and y = 4

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Akanksha Mishra  (9 years ago)

Sorry @tark,
but we cann't assume that a= --- and b= ---- now prove that

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