Question

Hey ! Here's a Math question to test you all !

If x+y=3 and x^2+y^2=15 then the value of (x-y)^2 will be ?

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Answer 1

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$\underline\bold{\huge{ANSWER \: :}}$

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Given expression : x+y = 3.


Let us see what will we get on squaring both sides of this given expression.

On doing so, we get :

(x+y)² = (3)²

=> x²+2xy+y² = 9

=> x²+y²+2xy = 9

=> 15 + 2xy = 9

=> 2 xy = 9-15

=> 2 xy = -6

=> xy = -6/2 or -3.

Now, we can find : (x-y)²

= x² - 2xy + y²

= x² + y² - 2 (-3)

= 15 + 6

= 21 [REQUIRED ANSWER]

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THUS, THE REQUIRED ANSWER IS 21.

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Answer 2

Answer:

(x-y)² = 21

Step-by-step explanation:

We have been given:-

x + y = 3            ...(1)

and

x² + y² = 15        ...(2)

We also know that,

( x + y )² = x² + y² + 2xy

In equation (1):-

Square on both sides :-

( x + y )² = 3²

( x + y )² = 9

Therefore,

x² + y² + 2xy = 9

Substitute the values from Equation (2):-

(15) + 2xy = 9

Transposing:-

2xy = 9 - 15

2xy = -6

xy = $\frac{-6}{2}$

xy = -3

We also know that,

(x - y)² = x² + y² - 2xy

Substitute the values:-

(x-y)² = (15) -2(-3)

(x-y)² = 15 + 6

(x - y)² = 21

So, the value of (x-y)² is 21 !

$\large\boxed{\large\boxed{\large\boxed{Solved !}}}}$