Question

Solve equations using structure

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Let m = x2 + 3.
Which equation is equivalent to (x2 + 3)2 + 7x2 + 21 =
10 in terms of m?

Answer 1

Answer:
`9m=10` or
`m=(10)/(9)`

I don't know your options... but you can check my work below and see if any of the other options fit yours.

Explanation:

`(x^2 + 3)2 + 7x^2 + 21 =10`

If
`x^2+3=m`, we can rewrite this as;

`(m)2+7x^2+21=10\\2m+7x^2+21=10`

By grouping, we can factor another m.

`2m+(7x^2+21)=10`

Factor a 7.

`2m+7(x^2+3)=10`

Rewrite it in terms of m.

`2m+7m=10`

Combine like terms;

`9m=10`

Divide by 9

`m=(10)/(9)`