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प्रश्न
Make z the subject of the formula y = `(2z + 1)/(2z - 1)`. If x = `(y + 1)/(y - 1)`, express z in terms of x, and find its value when x = 34.
उत्तर
y = `(2z + 1)/(2z - 1)`
⇒(2z - 1) y = 2z + 1
⇒ 2zy - y = 2z + 1
⇒ 2zy - 2z = 1 + y
⇒ z(2y - 1) = 1 + y
⇒ z = `(1 + y)/(2y - 1)`
⇒ x = `(y + 1)/(y - 1)`
⇒ x = `(((2z + 1)/(2z - 1)) + 1)/(((2z + 1)/(2z - 1)) - 1)`
= `(2z + 1 + 2z - 1)/(2z + 1 - 2z + 1)`
= `(4z)/(2)`
= 2z
⇒ z = `x/(2)`
Substituting x = 34, we get
z = `(34)/(2)`
= 17.
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