Make q the subject of the formula p=(2q^2-1)/(3q^2+2). Hence, find the value of q when p=1/2 given that q>0.
Solve for q:
p = (2 q^2-1)/(3 q^2+2)
p = (2 q^2-1)/(3 q^2+2) is equivalent to (2 q^2-1)/(3 q^2+2) = p:
(2 q^2-1)/(3 q^2+2) = p
Multiply both sides by 3 q^2+2:
2 q^2-1 = p (3 q^2+2)
Expand out terms of the right hand side:
2 q^2-1 = 2 p+3 p q^2
Subtract 3 p q^2-1 from both sides:
q^2 (2-3 p) = 2 p+1
Divide both sides by 2-3 p:
q^2 = (2 p+1)/(2-3 p)
Take the square root of both sides:
Answer: | q = sqrt((2 p+1)/(2-3 p)) or q = -sqrt((2 p+1)/(2-3 p))
IF p=1/2, then q=+or- 2
+426 \(p = \frac{2q^2-1}{3q^2+2} \\ \frac{1}{2} = \frac{2q^2-1}{3q^2+2}\\If \frac{a}{b}=\frac{c}{d},\quad then \,ad=bc. \\ 1(3q^2+2)=2(2q^2-1)\\Simplify\, and\,you\,get:\\ -q^2+4=0 \\ Using\,quadratic\,equation\,method,\, \\ we\,end\,up\,with:\\ q= \pm 2\)
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