Question

This is URGENT! Please help me solve this question with full solutions

Answer 1

B

Explanation:

Given

`(1)/((t-2)^2)` = 6 +
`(1)/((t-2))` ( multiply through by (t - 2)²

1 = 6(t - 2)² + t - 2 ← distribute parenthesis and simplify

1 = 6(t² - 4t + 4) + t - 2

1 = 6t² - 24t + 24 + t - 2

1 = 6t² - 23t + 22 ( subtract 1 from both sides )

6t² - 23t + 21 = 0 ← in standard form

(2t - 3)(3t - 7) = 0 → in factored form

Equate each factor to zero and solve for t

2t - 3 = 0 ⇒ 2t = 3 ⇒ t =
`(3)/(2)` ← p

3t - 7 = 0 ⇒ 3t = 7 ⇒ t =
`(7)/(3)` ← q

Thus

p × q =
`(3)/(2)` ×
`(7)/(3)` =
`(21)/(6)` =
`(7)/(2)` → B