Question

x-y=13 and √x+√y=13
Solve the equation

Answer 1

Answer is √x=13 And √y=0

Answer 2

The correct answer is x = 49 and y = 36.

Given: The equations = x-y=13 and √x+√y=13.

To Find: The value of x and y.

Solution:

√x+√y=13   (equation 1)

x-y=13  (equation 2)

$(\sqrt{x} )^{2} -(\sqrt{y} )^{2}=13$

Identity: $a^{2} -b^{2} =(a-b)(a+b)$.

By using the identity in the equation.

$(\sqrt{x} +\sqrt{y} )(\sqrt{x} -\sqrt{y} )=13$

Put the value of √x+√y from equation 1.

$13(\sqrt{x} -\sqrt{y} )=13$

$(\sqrt{x} -\sqrt{y} )=1$  (equation 3)

Add equation 1 and 3.

$\sqrt{x} +\sqrt{y}+\sqrt{x} -\sqrt{y} =1+13$

$2\sqrt{x} =14\\ \sqrt{x} =7$

x = 7x7 = 49

Subtract equation 1 and 3.

$\sqrt{x} +\sqrt{y}-\sqrt{x} +\sqrt{y} =13-1$

$2\sqrt{y} =12\\ \sqrt{y} =6$

y = 6x6 = 36

Hence, the value of x is 49 and that of y is 36.

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