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प्रश्न
Solve the following equation.
`[( 2x + 1)^2 + (2x - 1)^2]/[(2x + 1)^2 - (2x - 1)^2] = 17/8`
उत्तर
`[( 2x + 1)^2 + (2x - 1)^2]/[(2x + 1)^2 - (2x - 1)^2] = 17/8`
Applying componendo and dividendo, we get
`{[( 2x + 1)^2 + (2x - 1)^2] + [(2x + 1)^2 - (2x - 1)^2]}/{[( 2x + 1)^2 + (2x - 1)^2] - [(2x + 1)^2 - (2x - 1)^2]} = [17+8]/[17 - 8]`
⇒ `[2( 2x + 1)^2] /[2( 2x - 1)^2] = 25/9`
⇒ `(2x + 1)/( 2x - 1) = sqrt(25/9)`
⇒ `(2x + 1)/( 2x - 1) = 5/3`
⇒ `3(2x + 1) = 5(2x - 1)`
⇒ `6x + 3 = 10x - 5`
⇒ `10x - 6x = 5 + 3`
⇒ `4x = 8`
⇒ `x = 2`
Thus, the solution of the given equation is x = 2.
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