Question

$x {}^{2} + y { }^{2} = 4 \: andx + y = 2 \: \: then \: x \: y \: ki \: value$
​

Answer 1

Question : -

If x² + y² = 4 and x + y = 2 then the value of xy ?

ANSWER

Given : -

x² + y² = 4

x + y = 2

Required to find : -

• Values of xy ?

Solution : -

Since,

x + y = 2

Now, by squaring on both sides

(x + y)² = (2)²

• (a+b)² = a²+b²+2ab

x² + y² + 2xy = 4

But,

• x² + y² = 4

So,

4 + 2xy = 4

2xy = 4 - 4

2xy = 0

2*xy = 0/2

xy = 0

Therefore, value of xy = 0

____________________

Additional Information !

When you want to find the value of x & y for the above ..

Here x & y can take the value of zero respectively. So,

• Case (1)

When x = 0

since,

x + y = 2

0 + y = 2

» y = 2

x = 0 & y = 2

Similarly,

• Case (2)

When y = 0

x + y = 2

x + 0 = 2

» x = 2

x = 2 & y = 0

Answer 2

Given :-

• x² + y²  = 4
• x + y  = 2

To Find :-

• value of xy

Solution :-

❒ Here , in the question we're given the value of ( x + y ) which is 2

➼ We will do squaring on both the sides of this equation in order to find the value of  ( xy ) .

$\sf \mapsto (x+y)^{2} = (2)^{2}$

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

★ ( a + b )² = a² + b² + 2ab ★

$\sf \mapsto x^{2} +y^{2} + 2xy = 4$

➼ In this question we're given the value of ( x² + y² ) which is 4 , we can put this value in this equation .

$\sf \mapsto 4 + 2xy = 4$

➼ By transposing 4 on other side of equation . We'll get

$\sf \mapsto 2xy = 4 - 4$

$\sf \mapsto 2xy = 0$

➼ Let's divide 2 on both the sides of the equation .

$\sf \mapsto \dfrac{2xy}{2} = \dfrac{0}{2}$

$\sf \mapsto xy = 0$

∴ Value of xy is 0

More to know :-

➺ a² – b² = (a – b)(a + b)

➺ (a + b)² = a² + 2ab + b²

➺ a² + b² = (a + b)² – 2ab

➺ (a – b)² = a² – 2ab + b²

➺ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

➺ (a – b – c)² = a² + b² + c² – 2ab + 2bc – 2ca