Question

difference between a number and its positive square root is 12. Find the numbers

Answer 1

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

Answer 2

Question :

Difference between a number and its positive square root is 12. Find the number.

Answer :

The number is 16.

Given :

Difference between a number and its positive square root is 12.

To find :

The number

Solution :

Let the number be x

According to the problem,

x - √x = 12...........i

=> x - 12 = √x

Squaring both sides,

=> (x-12)^2 = (√x)^2

=> x^2 - 2.x.12 + (12)^2 = x .........applying the formula of

(a-b)^2 = a^2 - 2.a.b + b^2

=> x^2 -24x + 144 = x

=> x^2 -24x + 144 -x = 0

=> x^2 -25x + 144 = 0

=> x^2 -16x -9x + 144 = 0

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

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

Hence, x = wither 9 or 16

Putting the value of x as 9 in eq.i we find that only its negative root -3 satisfies , hence x cannot be 9.

Therefore, the number is 16.

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