Question

A natural number is greater than three times its square root by 4. Find the number​

Answer 1

16 is the natural number.... l guess so

Answer 2

Answer:

Let the natural number is =x=x then

According to given question.

x+3\times \sqrt{x}=4x+3×

x

=4

\Rightarrow x+3 \sqrt{x}=4⇒x+3

x

=4

\Rightarrow x-4=3 \sqrt{x}⇒x−4=3

x

Squaring both side and we get,

\Rightarrow x^{2}+16-8x=9x⇒x

2

+16−8x=9x

\Rightarrow x^{2}-8x-9x+16=0⇒x

2

−8x−9x+16=0

\Rightarrow x^{2}-17x+16=0⇒x

2

−17x+16=0

\Rightarrow x^{2}- (16+1)x+16=0⇒x

2

−(16+1)x+16=0

\Rightarrow x^{2}-16x-1x+16=0⇒x

2

−16x−1x+16=0

\Rightarrow x(x-16)-1(x-16)=0⇒x(x−16)−1(x−16)=0

\Rightarrow (x-16)(x-1)=0⇒(x−16)(x−1)=0

\Rightarrow x=1,16⇒x=1,16 (Natural no.)

Hence, this is the answer.