Question

Please Help. I'm confused.

Answer 1

b = 5, c = 13, d = 8.

Explanation:

The given expression is
`bx^(6) * cx^(12) * 9x^(d) = 585x^(26)`

Now, we have to solve for b, c, and d.

Here,
`bx^(6) * cx^(12) * 9x^(d) = 585x^(26)`

⇒
`9bcx^(6 + 12 + d) = 585x^(26)`

⇒
`9bcx^(18 + d) = 585x^(26)` ............. (1)

Now, comparing the base terms of both the sides of equation (1) we get,

9bc = 585

⇒ bc = 65 = 5 × 13

Therefore, b = 5 and c = 13 {Since b ≠ 1 and c ≠ 1 and c > b} (Answer)

Now, comparing the power terms of both the sides of equation (1), we get, 18 + d = 26

⇒ d = 8 (Answer)