Question

If x + y = 7 and xy = 3 , find the value of x² + y ²​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• If x + y = 7 and xy = 3 , find the value of ${x}^{2} \: + \: {y}^{2}$

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

We will use this identity here as x+ y and xy is given.

$\red{\boxed{ \sf \blue{ ( \: x \: + \: y \: )^{2} \: = \: (x) ^{2} \: + \: 2xy \: + {(y)}^{2} }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ {(7)}^{2} \: = \: {x}^{2} \: + \: 2xy \: + {y}^{2} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ {(7)}^{2} \: = \: {x}^{2} \: + \: {y}^{2} \: 2 \: \times \: 3 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 49 \: = \: {x}^{2} \: + \: {y}^{2} \: + \: 6 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 49 \: - \: 6 \: = \: {x}^{2} \: + \: {y}^{2} \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 49 \: - \: 6 \: = \: {x}^{2} \: + \: {y}^{2} \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{</p><p>43 \: = \: {x}^{2} \: + \: {y}^{2} \: }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ {x}^{2} \: + \: {y}^{2}\: = \: 43 }}}$

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Remember :-

• $\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: {x}^{2} \: + \: {y}^{2} \: = \: \frac{(x + y)^{2} \: + \: (x - y) ^{2} }{2} }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

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