Question

Select all of the values that are solutions of x2 + 20 = 12x.

Answer 1

. x² + 20 = 12x ⇔ x² - 12x + 20 = 0
D = b ² - 4 a c = 64,
. x₁, ₂ = (- b ± √D ) / ( 2a) = ( 12 ±√ 64) / 2 = ( 12 ± 8) / 2 ,
. x₁ = 10 , x ₂ = 2

Answer 2

2 and 10 are solutions of given expression
`x^2+20=12x`

Explanation:

Given expression
`x^2+20=12x`

We have to find the values that are solutions of given expression.

Since, the given expression is a quadratic equation , thus the roots are the solutions of given expression.

Consider the given expression ,
`x^2+20=12x`

It can be written as ,
`x^2-12x+20=0`

We can solve the given quadratic equation using middle term splitting method,

-12x can be written as -2x - 10x

`x^2-12x+20=0\\\\ x^2-2x-10x+20=0\\\\`

`x^2-12x+20=0`

taking x common from first two terms and -10 common from last two terms, we have,

`x(x-2)-10(x-2)=0`

`\Rightarrow (x-2)(x-10)=0`

using zero product property, we have,
`ab=0 \Rightarrow a=0\ or\ b=0`

`\Rightarrow (x-2)=0` or
`\Rightarrow (x-10)=0`

`\Rightarrow x=2` or
`\Rightarrow x=10`

Thus, 2 and 10 are solutions of given expression
`x^2+20=12x`