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Question
If 2x = 4y = 8z and `1/(2x) + 1/(4y) + 1/(8z) = 4` , find the value of x.
Solution
2x = 4y = 8z and `1/(2x) + 1/(4y) + 1/(8z) = 4`
2x = 4y = 8z
⇒ 2x = 22y = 23z
⇒ x = 2y = 3z
⇒ y = `x/2 and z = x/3`
Now, `1/(2x) + 1/(4y) + 1/(8z) = 4`
⇒ `1/(2x) + 1/[(4x)/2] + 1/[(8x)/3] = 4`
⇒ `1/(2x) + 2/(4x) + 3/(8x) = 4`
⇒ `1/(2x) + 1/(2x) + 3/(8x) = 4`
⇒ `[ 4 + 4 + 3 ]/(8x) = 4`
⇒ `11/(8x) = 4`
⇒ x = `11/32`.
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