Question

If x-y=7 and xy=9, find the value of x²+y².​

Answer 1

$\bf \LARGE \color{pink}Hola!$

GiveN :

$\sf \mapsto \: (x - y) = 7$

$\sf \mapsto \: xy = 9$

To FinD :

$\sf \mapsto \: {x}^{2} + {y}^{2} = {?}$

SolutioN :

$\:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \sf \:  {(x - y)}^{2}  = 7^{2}$

$\implies \sf \:  {x}^{2}  +  {y}^{2}  - 2xy = 49$

$\sf \implies \:  {x}^{2}  +  {y}^{2}  - 2 \times 9 = 49 \:  \:  \:  \:  \:  \bf[ \:  Given   \:  \:  ;\: \: xy = 9 \: ]$

$\: \: \: \: \: \: \: \: \sf \therefore{ \underline{ \boxed {\sf{ {x}^{2} + {y}^{2} = 67}}}}$

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HOPE THIS IS HELPFUL...

Answer 2

hello mate...

Answer...

Given

• x - y = 7
• xy = 9

To Find

• Find the value of x²+y²

Solution

[using identity] ( a - b )² = a² - 2ab + b²

x - y = 7

lets squared both sides...

( x - y )² = ( 7 )²

= x² + y² - 2xy = 49

= x² + y² - 2 × 9 = 49

= x² + y² - 18 = 49

= x² + y² = 49 + 18

= x² + y² = 67

Hence,

The value of x² + y² = 67