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If 4x+5y=23 and xy =6,find the value of 16x^2+25y^2. |
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Answer» 4x + 5y = 23 xy = 6, => y = 6 / X Substituting value of y = 6 / x in the first equation we get, 4x + 5 ( 6 / x ) = 23 4x + 30 / x = 23 Taking LCM we get, 4x² + 30 / x = 23 4x² + 30 = 23 x => 4x² - 23x + 30 = 0 => 4x - 15x - 8x + 30 = 0 => x ( 4x - 15 ) - 2 ( 4x - 15 ) = 0 => ( 4x - 15 ) ( x - 2 ) = 0 => x = 15 / 4 ; 2 Taking X = 2 we get y = 6 / 2 = 3 So value of 16x² + 25y² is : 16 ( 2 )² + 25 ( 3 )² 16 * 4 + 25 * 9 64 + 225 289 |
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