Question

root x+5+ root x-16/root x+5- root x-16=7/3 prove x=20​

Answer 1

Answer:

proved

Step-by-step explanation:

root x+5+ root x-16/root x+5- root x-16=7/3

√ x + 5+√x-16/√ x+5- √ x-16 = 7/3

√ x + 5+√x-16 ÷ √ x+5 - √ x-16 = 7/3

multiply and divide by the conjugate of the LHS

{√(x+5) + √(x-16)}² ÷  (x+5) - (x-16)

2x -11 + 2√(x² - 11x-80) = 21×7/3 = 49

2√(x² - 11x-80 )= 60-2x

x² - 11x-80 = (30- x)² = x² - 60x +900

49 x = 980

x = 980 ÷ 49

x = 20