Question

Difference between a number and its positive square root is 6. Find the number.

Answer 1

Given question,

x - √x = 6


=> x - √x - 6 = 0

Now using the "Splitting the middle term" method,

We get

x - √x - 6 = 0

=> x - 3√x + 2√x - 6 = 0

=> √x(√x- 3) + 2(√x - 3) = 0

=> (√x + 2)(√x - 3) = 0

Now,

(√x + 2)(√x - 3) = 0

=> √x + 2 = 0/(√x - 3)

=> √x + 2 = 0

=> √x = -2

But it's given that the root is positive
so,

√x ≠ -2

Again,

(√x + 2)(√x - 3) = 0

=> √x - 3 = 0/(√x + 2)

=>√x - 3 = 0

=> √x = 3

=> x = (3)²

=> x = 9


So the number is 9.


Hope it helps dear friend ☺️✌️

Answer 2

Let  that  number be  x²

positive square root  of  number =  x

We know that, square  root  of  an number  it  less than  that number ,

x < x²

According  to question, difference  between number  and  its positive  square is  6

x² - x  = 6

x² - x  - 6 = 0

x² -3x +2x - 6 = 0

x(x - 3) +2(x-3) = 0

(x-3)(x+4) = 0

x = -4 (negligible)

x = 3

So the Number  = x² = 3² = 9