Question

The sum of twice a number and 1 is equal to 3 times the positive square root of the number find the number

Answer 1

let the number be "x"
then the given condition can be mathematically expressed as:
\[(2x)+1=3\sqrt{x}\\
\text{squaring both sides...}\\
4x^2+4x+1=9x\\
4x^2-5x+1=0\\
4x^2-4x-x+1=0\\
4x(x-1)-(x-1)=0\\
(4x-1)(x-1)=0\\
4x-1=0\qquad{\rm OR}\qquad x-1=0\\
x={1\over4}\qquad{\rm OR}\qquad \boxed{\Large x=1}
\]
we choose the second since "x" is a number and not a fraction

Answer 2

ok i see thank you so much!!

Answer 3

yw