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umka21 [38]
3 years ago
5

Make x the subject of the formula

Mathematics
1 answer:
kupik [55]3 years ago
8 0

Answer:

\boxed{x  =  \frac{p + q {r}^{2} }{a - b {r}^{2} } }

Step-by-step explanation:

Solve  \: for  \: x: \\  =  > r =  \sqrt{ \frac{ax - p}{q + bx} }  \\  \\ r =  \sqrt{ \frac{ax - p}{q + bx} }  \:  is \:  equivalent \: to \:   \sqrt{ \frac{ax - p}{q + bx} }  = r :\\  =  > \sqrt{ \frac{ax - p}{q + bx} }  = r \\  \\ Raise \:  both \:  sides  \: to \:  the  \: power \:  of  \: two:  \\ =  >   \frac{ax - p}{q + bx}  =  {r}^{2} \\  \\ Multiply  \: both  \: sides \:  by  \: (q + b x):  \\  =  > ax - p =  {r}^{2} (q + bx) \\  \\ Expand  \: out \:  terms \:  of  \: the \:  right  \: hand  \: side:  \\ =  >  ax - p = q {r}^{2} + b {r}^{2}x \\  \\ Subtract \:  b {r}^{2}x - p \:   from \:  both \:  sides:  \\  =  >   x(a - b {r}^{2} ) = p + q {r}^{2}  \\  \\  Divide \:  both \:  sides  \: by \:  a - b {r}^{2} :  \\  =  > x  =  \frac{p + q {r}^{2} }{a - b {r}^{2} }

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