Question

(x-y)² =144 and xy=46, find the value of x² + y². ​

Answer 1

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Answer:

$x^{2} +y^{2} =236$

Step-by-step explanation:

$(x-y)^{2} =144$

⇒ $x^{2} +y^{2} -2xy=144$          [∵ $(a-b)^{2} =x^{2} +y^{2} -2ab$]

⇒ $x^{2} +y^{2} -2(46)=144$        [∵ $xy=46$ as given in the question]

⇒ $x^{2} +y^{2} -92=144$  

⇒ $x^{2} +y^{2} =144+92$

⇒ $x^{2} +y^{2} =236$

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Answer 2

x^2+ y^2
=(x-y)^2+2.x.y
=144+2*46
=144+92
=236