Question

A survey was done in a small area in which √(5 + 2x) votes were men
and
9/
√(5+2x)
votes were women. Find x, if the number of men is equal to the number of

women.

Answer 1

9+2x

−

2x

=

9+2x

5

⇒x≥0 & x≥−9/2

⇒9+2x−

(9+2x)2x

=5

⇒2x+4=

(9+2x)2x

Squaring

⇒4x

2

+16x+16=(9+2x)2x

⇒4x

2

+16x+16=4x

2

+18x

⇒

x=8

Answer 2

NUMBERS

Given:

√(5 + 2x) votes were men and  9/ √(5+2x)  votes were women.

To Find:

Value of x.

Explanation:

Given that, the number of men is equal to number of women.

$\sqrt{5+2x} =\frac{9}{\sqrt{5+2x} } \\\\\implies on \ squaring \ both\ sides\\\\5+2x=\frac{81}{5+2x}\\\\\implies 25+4x^{2} +20x = 81\\\\\implies4x^{2} +20x=56\\\\\implies x^{2} +5x-14=0\\\\\implies x^{2} +7x-2x-14=0\\\\\implies x(x+7)-2(x+7)=0\\\\ \implies(x+7)(x-2)=0\\\\\implies x=-7 \ and \ x=2$

-7 is not an feasible for answer.

Hence the feasible value of x is 2.