Question

√x = √3x
What is the solution to the equation above?

Answer 1

`\sf \: x = (1)/(3) \: (or) \: x = 0`

Explanation:

The equation given is,

→ √x = √3x

Now the value of x will be,

→ √x = √3x

→ x = (√3x)²

→ x = 3x²

→ 3x² = x

→ 3x² - x = 0

→ (3x - 1)(x) = 0

→ 3x - 1 = 0 || → x = 0

→ 3x = 0 + 1 || → [ x = 0 ]

→ 3x = 1 ||

→ [ x = 1/3 ] ||

These are the values of x.

Answer 2

`x=0,\;x=(1)/(3)`

Explanation:

Given equation:

`√(x)=√(3)x`

Square both sides:

`\implies \left(√(x)\right)^2= \left(√(3)x\right)^2`

`\implies x= \left(√(3)\right)^2 \cdot \left(x\right)^2`

`\implies x=3x^2`

Subtract x from both sides:

`\implies x-x=3x^2-x`

`\implies 0=3x^2-x`

`\implies 3x^2-x=0`

Factor out the common term x:

`\implies x(3x-1)=0`

Apply the zero-product property:

`\implies x=0`

`\implies 3x-1=0 \implies x=(1)/(3)`