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प्रश्न
Solve the following equation.
`[(3x - 4)^3 - ( x + 1)^3]/[( 3x - 4)^3 + ( x + 1)^3] = 61/189`
उत्तर
`[(3x - 4)^3 - ( x + 1)^3]/[( 3x - 4)^3 + ( x + 1)^3] = 61/189`
Applying componendo and dividendo, we get
`{[(3x - 4)^3 - ( x + 1)^3] + [( 3x - 4)^3 + ( x + 1)^3]} /{[(3x - 4)^3 - ( x + 1)^3] - [( 3x - 4)^3 + ( x + 1)^3]} = (61 + 189) /(61 - 189)`
⇒ `{2 ( 3x - 4)^3}/{-2( x +1)^3} = 250/-128`
⇒ `{(3x - 4)^3}/( x + 1)^3 = 125/64`
Taking cube root on both sides, we get
`therefore (3x -4)/(x + 1) = root(3)(125/64)`
⇒ `(3x - 4)/(x + 1)= root(3)[(5/4)^3]`
⇒ `(3x - 4)/(x + 1) = 5/4`
⇒ 4(3x - 4) = 5(x + 1)
⇒ 12x - 16 = 5x + 5
⇒ 12x - 5x = 16 + 5
⇒ 7x = 21
⇒ x = 3
Thus, the solution of the given equation is x = 3.
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