Question

If x-y=1 and x2+y2=41, find the value of x+y.​

Answer 1

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Answer 2

$\sf{\underline{\boxed{\green{\large{\bold{ Given}}}}}}$

• $\sf x - y = 1$
• $\sf x^2 + y^2 = 41$

$\sf{\underline{\boxed{\green{\large{\bold{ To\: Find}}}}}}$

• x + y = ??

$\sf{\underline{\boxed{\green{\large{\bold{ solution}}}}}}$

$\sf{\underline{\boxed{\pink{\large{\mathfrak{( x - y ) ^2 = x^2 + y^2 - 2xy }}}}}}$

$\sf \implies 1^2 = 41 - 2xy$

$\sf\implies 2xy = 41 - 1$

$\sf\implies 2xy = 40$

$\sf\implies xy = \dfrac{40}{2}$

$\sf\implies xy = 20$

$\sf{\underline{\boxed{\pink{\large{\mathfrak{( x + y )^2 - ( x - y )^2 = 4xy }}}}}}$

$\sf\implies ( x + y )^2 - ( 1 )^2 = 4 \times 20$

$\sf\implies ( x + y )^2 - 1 = 80$

$\sf\implies ( x + y )^2 = 81$

$\sf\implies x + y = \sqrt{81}$

$\sf{\underline{\boxed{\green{\large{\mathfrak{ x + y = \sqrt{81}}}}}}}$