Question

if 3x^2+3y^2= 42 and xy=-15. find the value of (x-y)^2

Answer 1

SOLUTION

GIVEN

3x² + 3y² = 42 and xy = - 15

TO DETERMINE

The value of ( x - y )²

EVALUATION

Here it is given that

3x² + 3y² = 42 and xy = - 15

Now

3x² + 3y² = 42

⇒ 3(x² + y²) = 42

⇒ (x² + y²) = 14

Therefore

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

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

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

$\sf{ = 14 - 2 \times ( - 15)}$

$\sf{ = 14 + 30}$

$\sf{ = 44}$

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Answer 2

Step-by-step explanation:

$Here it is given that</p><p></p><p>3x² + 3y² = 42 and xy = - 15</p><p></p><p>Now</p><p></p><p>3x² + 3y² = 42</p><p></p><p>⇒ 3(x² + y²) = 42</p><p></p><p>⇒ (x² + y²) = 14</p><p></p><p>Therefore</p><p></p><p>\sf{ {(x - y)}^{2} }(x−y) </p><p>2</p><p> </p><p></p><p>\sf{ = {x}^{2} - 2xy + {y}^{2} }=x </p><p>2</p><p> −2xy+y </p><p>2</p><p> </p><p></p><p>\sf{ = {x}^{2} + {y}^{2} - 2xy}=x </p><p>2</p><p> +y </p><p>2</p><p> −2xy</p><p></p><p>\sf{ = 14 - 2 \times ( - 15)}=14−2×($

−15)