Question

The number of solutions of the system
of equations given below is x + y) = 1,
x² + y² = a²
​

Answer 1

Answer:

a²=1-2xy

Step-by-step explanation:

(x+y) ²=1²

or, x²+2xy+y²= 1

or x²+y²=1-2xy

compare with the equation between x²+y²=a², we get----

a²=1-2xy

Answer 2

The solution is $a^{2}=1-2xy$

Step-by-step explanation

Given,

$x^{2}+y^{2} =a^{2}$

And x+y=1

Now,

$a^{2}=(x+y)^{2}-2xy$

$\because x+y=1$

$\therefore a^{2}=(1)^{2}-2xy$

⇒$a=+\sqrt{1-2xy} ,-\sqrt{1-2xy}$

Therefore, the answer is $a^{2}=1-2xy$.