Question

Solving Equation 7(√x/1-x) + 8(√1-x/x) = 15 following roots obtained

Please Give Full Solution

Correct Answer is (a) 64/113 & 1/2​

Answer 1

Step-by-step explanation:

7[√(x/1+x)] + 8 [√(1-x)/x ] = 15

put y = √(x/1-x), then the equation reduces to,

7y + 8/y = 15

=> 7y² + 8 = 15y [ multiply both sides by y ]

=> 7y² - 15y + 8 = 0

=> 7y² - 8y - 7y + 8 = 0

=> y (7y - 8) - 1 ( 7y - 8) = 0

=> (y - 1)(7y - 8) = 0

=> y - 1 = 0 => y = 1

and

=> 7y - 8 = 0 => y = 8/7

now get back the values of x by resubstitution

y = √(x/1-x) = 1 => x/1-x = 1 [ squaring both sides ]

=> x = 1-x => 2x = 1 => x = 1/2 answer 1

y = √(x/1-x) = 8/7 => x/1-x = 64/49 [squaring both sides ]

=> 64(1-x) = 49(x)

=> 64 - 64x = 49x

=> 64 = 49x + 64x

=> 64 = 113x

=> x = 64/113 answer 2