An algebra problem by Saurav Pal

Algebra Level 2

If p>q>0 are two real numbers, then the value of p q + ( p − q ) p q + ( p − q ) p q + ( p − q ) p q + ( p − q ) . . . . . \sqrt{pq+(p-q)\sqrt{pq+(p-q)\sqrt{pq+(p-q)\sqrt{pq+(p-q)\sqrt{. . . . .}}}}} is-

independent of p independent of q dependent on both p and q independent of both p and q

Saurav Pal by Saurav Pal , 26, India

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1 solution

Rajen Kapur
Apr 27, 2015

Let it be equal to y. Squaring both sides and putting y in the r.h.s. for the expression in the brackets: y^2 = pq + (p - q) y, or (y - p) (y + q) = 0. Taking positive value of y, the solution is y = p i.e. independent of q.

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