Question

using the properties of proportion, solve the equation 5x+(x2-1)/5x-(x2-1)=7/5(2here refer to square and "/" refer to upon )​

Answer 1

Given :   5x + (x² - 1) / (5x - (x² - 1)   = 7/5

To Find : x

Solution:

5x + (x² - 1) / (5x - (x² - 1)   = 7/5

a/b = c/d

using Componendo-Dividendo

=> a + b/(a - b)   =  c + d / c - d

a = 5x + (x² - 1)

b =  (5x - (x² - 1)

a + b =  10x

a - b  =  2(x² - 1)

c = 7

d = 5

c + d = 12

c - d =  2

10x/2(x² - 1)   = 12/2

=> 5x/(x² - 1)   = 6

=> 5x = 6x² - 6

=>  6x² - 5x - 6  = 0

=> 6x² -9x + 4x - 6  = 0

=> 3x(2x - 3) + 2(2x - 3) = 0

=> (3x + 2)(2x - 3) = 0

=> x = - 2/3  , x = 3/2

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Answer 2

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