Question

Find the value of 121x^2 + 144y^2, if (11x + 12y) = 34 and xy = 2.​

Answer 1

Step-by-step explanation:

$121 {x}^{2} + 144 {y}^{2} = {(11x)}^{2} + {(12y)}^{2}$

By the identity,

${(x + y)}^{2} = (x + y)(x + y)$

${(11x)}^{2} + {(12y)}^{2} = (11x + 12y)(11x + 12y)$

Given that 11x + 12y = 34...

Substituting the above value, we get,

$(11x + 12y)(11x + 12y) = (34)(34) = 1156$

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