InterviewSolution
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InterviewSolution
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Solve the equations :(x - 4) (y - 4)= 16(y - 6) (z - 6)= 36(z - 8) (x - 8) = 64. |
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Answer» Solution :We have,(x - 4) (y - 4) = 16 implies XY - 4x - 4y + 16 = 16 implies4(x+y) = xy implies`(x+y)/(xy)=(1)/(4)""(because xy ne 0)` implies`(1)/(x) + (1)/(y) = (1)/(4) "" ….(1)` Also,(y - 6)(z - 6) = 36 impliesyz - 6y - 6z + 36 = 36 implies 6(y + z) = yz implies`(y+z)/(yz)=(1)/(6)""(because yz ne 0)` implies`(1)/(z) + (1)/(y) = (1)/(6) ""....(2)` and(z - 8) (z - 8) = 64 implies xz - 8Z - 8x + 64 = 64 implies implies8(x + z) = xz implies`(x + z)/(xz) = (1)/(8) ""(because zx ne 0)` implies`(1)/(z) + (1)/(x) = (1)/(8)""....(3)` Adding equations (1), (2) and (3), we get `2((1)/(x) + (1)/(y) + (1)/(z)) = (1)/(4) + (1)/(6) + (1)/(8)` implies `(1)/(x) + (1)/(y) + (1)/(z) = (6+4+3)/(24) xx (1)/(2)` implies`(1)/(x) + (1)/(y) + (1)/(z) = (13)/(48)"....(4)"` `therefore`From equations (1) and (4), we get `(1)/(4) + (1)/(z) = (13)/(48)implies(1)/(z) = (13)/(48) - (1)/(4) = (1)/(48)` `therefore z = 48`. From equations (2) and (4), we get `(1)/(6) + (1)/(x) = (13)/(48)` implies`(1)/(x) = (13)/(48) - (1)/(6) = (5)/(48)` ` implies x = (48)/(5)` From equations (3) and (4), we get `(1)/(8) + (1)/(y) = (13)/(48)` implies `(1)/(y) = (13)/(48)-(1)/(8) = (7)/(48)` `thereforey = (48)/(7)` So, `x = (48)/(5), y = (48)/(7), z = 48` |
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