Question

Let m=x^2-5m=x 2 −5m, equals, x, squared, minus, 5. Which equation is equivalent to (x^2-5)^2-3x^2+15=-2(x 2 −5) 2 −3x 2 +15=−2left parenthesis, x, squared, minus, 5, right parenthesis, squared, minus, 3, x, squared, plus, 15, equals, minus, 2 in terms of m ?

Answer 1

• 
  `m^2-3m=-2`
• 
  `m^2-3m+2=0`

Explanation:

Let
`m=x^2-5`

We want to express the equation
`(x^2-5)^2-3x^2+15=-2` in terms of m.

Given:
`(x^2-5)^2-3x^2+15=-2`

Factorizing the third and fourth term, we obtain:

`(x^2-5)^2-3(x^2-5)=-2`

Substituting
`m=x^2-5`, the above equation becomes:

`m^2-3m=-2`

Since the options are not given, the equivalent equation is:

`m^2-3m=-2`

It could also be written in a rearranged form as:

`m^2-3m+2=0`