Question

Difference between a number and its positive square root is 12. Find the number. topic:Quadratic equation

Answer 1

Answer:

Let the number be 'x'.

ATQ

x - √x =12     eq(1)

x - 12 = √x

square both sides

(x - 12)² = x

x² - 24x + 144 = x

x² - 25x + 144 = 0

x² -16x - 9x +144 = 0

x(x-16) -9(x-16) = 0

(x-9)(x-16)=0

x= 9,16

by putting x = 9 in eq 1 we see that only its negative root i.e -3 satisfies.

so 9 cannot be the ans.

9 -√9 = 9 - 3=6 ≠12

16 - √16 =12

So,correct ans is 16