CBSE Class 9 Answered

x =[ (p+2q) + (p-2q)] / [ (p+2q) - (p-2q)]

x [(p+2q)  - (p-2q)] = [(p+2q) + (p-2q)]

multiply both sides with [(p+2q) + (p-2q)]

x [(p+2q)  - (p-2q)]² = [(p+2q) + (p-2q)] [(p+2q) - (p-2q)]

x [ p + 2q + p - 2q - 2(p+2q)(p-2q) = (p+2q) - (p-2q)

2px - 2x (p+2q)(p-2q) = p + 2q - p + 2q

2px - 4q = 2x(p+2q)(p-2q)

px - 2q = x(p+2q)(p-2q)

squaring both sides we get

p²x² + 4q² - 4pqx = x² (p² - 4q²)

p²x² + 4q² - 4pqx - p²x² + 4q²x² = 0

4q² - 4pqx + 4q²x² = 0

q² - pqx + q²x² = 0

q - px + qx² = 0

qx² -px + q = 0