Question

If x + y = 12 and xy = 32, then what is the value of x2 + y2 ?

A) 24 B) 144 C) 128 D) 80

Answer 1

Given :

• x + y = 12
• xy = 32

To find :

• Value of x² + y² .

Solution :

• x + y = 12
• xy = 32

Now find the value of x² + y² .

$\to\sf{x^2+y^2}$

• Use identity : a² + b² = (a+b)² - 2ab

$\to\sf{(x+y)^2-2xy}$

• Put values : x+y = 12 and xy = 32

$\to\sf{(12)^2-2\times\:32}$

$\to\sf{144-64}$

$\to\sf{80}$

Therefore, the value of x² + y² is 80.

${\boxed{\bold{Option\:D)80\:is\: Correct\: Answer.}}}$

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Some identities :-

★ (a+b)² = a² + 2ab + b²

★ (a-b)² = a² -2ab + b²

★ a² + b² = (a+b)² - 2ab

★ a² + b² = (a-b)² + 2ab

★ a² - b² = (a+b) (a-b)