Question

If x+11y =7 and xy = 2, find the value of x2 + 121y2

Answer 1

x + 11y = 7-----equation(1)

xy = 2 -------equation(2)

Squaring on both on equation (1)

(x+11y)^2 = 7^2

=> x^2 + (11y)^2 + 2(x)(11y) = 49

[ ∵ (a+b)^2 = a^2 + b^2 + 2ab]

=> x^2 + 121y + 22xy = 49

Put the value of xy from equation(2) ,

=> x^2 + 121y + 22(2) = 49

=> x^2 + 121y + 44 = 49

=> x^2 + 121y = 49 - 44

=> x^2 + 121y = 5