2022 · Q4
If (√(x+20)+√(x-1))/(√(x+20)-√(x-1))=(7)/(3), then what is the value of √((x+20)(x-1))?
Elementary MathematicsAlgebra
- A8
- B9
- C10
- D12
Explanation
Apply componendo–dividendo: √(x+20)/√(x−1) = (7+3)/(7−3) = 5/2. Squaring gives (x+20)/(x−1) = 25/4, so 4x+80 = 25x−25 and x = 5. Then √((x+20)(x−1)) = √(25·4) = 10. The keyed option is C.