Question

$x + \sqrt{x } = 132$

Answer 1

x + √x = 132

.

Define y:

Let y = √x

.

Substitute √x as y:

y² + y = 132

y² + y - 132 = 0

(y - 11)(y + 12) = 0

y = 11 or y = -12 (rejected)

.

Find x:

y = √x

x = y²

.

When y = 11,

x = (11)²

x = 121

.

Answer: x = 121

Answer 2

suppose requires natural number =x

sum of natural number and its square root =x+x

putting 

x=yx=y2

y2+y=132y2+12y−11y−132=0y(y+12)−11(y+12)=0(y+12)(y−11)y=11x=11x=(11)2x=121