Solve equations using structure You might need: Calculator Let m = x2 + 3. Which equation is equivalent to (x2 + 3)2 + 7x2 + 21 = 10 in terms of m?

Question

asked Dec 12, 2021 50.8k views

1 Answer

Remul · Answer 1 · 2021-12-18T08:02:40+0000

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)