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प्रश्न
Solve the following equation.
`[(4x +1)^2 + ( 2x + 3)^2]/[4x^2 + 12x + 9] = 61/36`
उत्तर
` [(4x +1)^2 + ( 2x + 3)^2]/[4x^2 + 12x + 9] = 61/36`
⇒ ` [(4x +1)^2 + ( 2x + 3)^2]/[(2x)^2 + 2 (2x) (3) + 3^2] = 61/36`
⇒ ` ((4x +1)^2 + ( 2x + 3)^2)/(2x + 3)^2 = 61/36`
Applying dividendo, we get
⇒ `{(4x +1)^2 + ( 2x + 3)^2 - (2x + 3)^2}/( 2x + 3)^2 = (61 - 36)/36`
⇒ `[(4x + 1)^2]/[( 2x + 3 )^2] = 25/36`
Taking square root on both sides, we get
⇒ `( 4x + 1)/(2x + 3) = sqrt (25/36) = 5/6`
⇒ `(4x + 1)/(2x + 3) = 5/6`
⇒ `6(4x + 1) + 5(2x + 3)`
⇒ `24x + 6 = 10x + 15`
⇒ `24x - 10x = 15 - 6`
⇒ `14x = 9`
⇒ `x =9/14`
Thus, the solution of the given equation is x = `9/14`.
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