## Trending News

# Help with algebra question?

If 3x^3 + ax^2 + 5x = 3(x+b)^3 + c, find all possible values of a, b, and c.

### 3 Answers

- PinkgreenLv 76 months ago
Hint: expand the right hand side & compare

the coefficients.

- Login to reply the answers

- KrishnamurthyLv 76 months ago
3x^3 + ax^2 + 5x = 3(x + b)^3 + c

a x^2 + 3 x^3 + 5 x = 3 b^3 + 9 b^2 x + 9 b x^2 + c + 3 x^3

a = -3 sqrt(5), b = -sqrt(5)/3, c = (5 sqrt(5))/9

a = 3 sqrt(5), b = sqrt(5)/3, c = -(5 sqrt(5))/9

- Login to reply the answers

- husoskiLv 76 months ago
Expand the right side:

3x^3 + ax^2 + 5x = 3(x^3 = 3bx^2 + 3b^2x + b^3) + c

(3x^3 + ax^2 + 5x = (3)x^3 + (9b)x^2 + (9b^2)x + (3b^3 + c)

Equate coefficients on like powers of x:

3 = 3

a = 9b

5 = 9b^2

0 = 3b^3 + c

The the third line says that b must be ±(√5)/3. Then line 2 says

a = 9b = ±3√5 . . . . same sign as b

c = -3b^3 = - ± 3(5√5) / (3^3) = - ±5√5 / 9. . . . opposite sign of b

So (a, b, c) = (3√5.√5 / 3, -5√5 / 9) or (-3√5, -√5 / 3, 5√5 / 9).

- Login to reply the answers