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प्रश्न
Solve :
`[2xy]/[ x + y ] = 3/2`
`[xy]/[ 2x - y ] = -3/10`
x + y ≠ 0 and 2x - y ≠ 0
उत्तर
`[2xy]/[ x + y ] = 3/2`
⇒ `[ x + y ]/[ xy ] = 4/3`
⇒ `1/x + 1/y = 4/3` .....(1)
`[xy]/[ 2x - y ] = -3/10`
⇒ `[ 2x - y ]/[ xy ] = - 10/3`
⇒ `-1/x + 2/y = - 10/3` ......(2)
Let `1/x = u and 1/y = v`
Then, equations (1) and (2) become
u + v = `4/3 and - u + 2v = - 10/3`
⇒ 3u + 3v = 4 and -3u + 6v = -10
Adding, We have
9v = - 6
⇒ v = `-6/9 = - 2/3`
⇒ `1/y = - 2/3 `
⇒ y = `-3/2`
Substituting y = `-3/2` in (1), We have
`1/x - 2/3 = 4/3`
⇒ `1/x = 6/3 = 2`
⇒ x = `1/2`
Hence, x = `1/2 and y = - 3/2`
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