Question

if x+y=5 and xy =-1then find the value of x^2+y^2​

Answer 1

Given

• x + y = 5
• xy = -1

To Find

• x² + y²

Solution

$\tt \implies \: x + y = 5 \\ \tt \implies \: (x + y) {}^{2} = (5) {}^{2} .........(squaring \: both \: sides) \\ \tt \implies \: x {}^{2} + y {}^{2} + 2xy = 25 \\ \: \tt \implies \: x {}^{2} + y {}^{2} + 2( - 1) = 25...........(given \: xy = - 1) \\ \tt \implies \: x {}^{2} + y {}^{2} - 2 = 25 \\\tt \implies \: x {}^{2} + y {}^{2} = 25 + 2$

$\large \implies \boxed {\boxed {\tt \blue {x {}^{2} + y {}^{2} = 27 }}}$

➣Final Answer

x² + y² = 27

Used identity

(x+y)² = x² + y² +2xy

Answer 2

${\underline{\huge{\mathbf{\color{pink}{Question}}}}}$

if x+y=5 and xy =-1then find the value of$x^2+y^2$

${\underline{\huge{\mathbf{\color{pink}{solution}}}}}$

Given :-

x + y = 5

xy = -1

To find :-

$x^2 + y^2$

Formulae used:-

$(x+y)^2 = x^2 + y^2 + 2xy$

step by step solution :-

$(5)^2 = x^2 + y^2 + 2*-1$

$25 = x^ 2 + y^2 -2$

$x^2 + y^2 = 25 + 2$

$x^2 + y^2 = 27$

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Thank you ❤