"if p:q is the sub-duplicate ratio of p-x2:q-x2 then x2 is ?"
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Answered by
191
p/q = √(p - x^2)/√(q - x^2)
p^2/q^2 = (p - x^2)/(q - x^2)
Cross multiply
(p^2)*(q - x^2) = (q^2)*(p - x^2)
p^2*q - p^2*x^2 = q^2*p - q^2*x^2
p^2*q - q^2*p = p^2*x^2 - q^2*x^2
pq(p - q) = x^2*(p^2 - q^2)
pq(p - q) = x^2*(p + q)(p - q)
pq = x^2*(p + q)
X^2 = pq/(p + q)
Answered by
70
p/q = √(p - x^2)/√(q - x^2) p^2/q^2 = (p - x^2)/(q - x^2) Cross multiply (p^2)*(q - x^2) = (q^2)*(p - x^2) p^2*q - p^2*x^2 = q^2*p - q^2*x^2 p^2*q - q^2*p = p^2*x^2 - q^2*x^2 pq(p - q) = x^2*(p^2 - q^2) pq(p - q) = x^2*(p + q)(p - q) pq = x^2*(p + q) X^2 = pq/(p + q)
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