Question

Solving equation 7√x/1-x + 8√1-x/x = 15 following roots are obtained

Answer 1

Given:

The equation 7√x/1-x + 8√1-x/x = 15  

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To find:

Solving equation 7√x/1-x + 8√1-x/x = 15 following roots are obtained

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Solution:

From given, we have,

The equation 7√x/1-x + 8√1-x/x = 15  

7√x/1-x + 8√1-x/x = 15

multiplying the denominators of LHS, we get,

7(√x)² + 8(√1-x)² / √x √1-x = 15

7x + 8(1 - x) = 15 (√x √1-x)

7x + 8 - 8x = 15 (√x √1-x)

8 - x = 15 (√x √1-x)

squaring on both the sides, we get,

(8 - x)² = 15² (√x √1-x)²

64 + x² - 16x = 225 [x (1 - x)]

64 + x² - 16x = 225 (x - x²)

64 + x² - 16x = 225x - 225x²

226x² - 241x + 64 = 0

solving the above quadratic equation, we get,

x = 64/113, x = 1/2

Therefore, the roots of the equation 7√x/1-x + 8√1-x/x = 15 are x = 64/113, x = 1/2

Answer 2

The Value of x = 64/113 , 1/2