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If the ratio of the roots of lx^2-nx+n=0 is p:q then prove that.   √p/√q  + √q/√p- √n/√l=0
 
3 months ago

Answers : (1)

Arun
23020 Points
							
To solve the question, proceed in the following manner- 
Let a and b be those two roots of the given equations. 
√(p/q) + √(q/p) + √(n/l) can be written as,  √p/√q + √q/√p + √n/√l
= (√p² + √q² )/(√p*√q) + √n/√l
= (p + q)/(√p*√q) + √n/√l ...................(1)
Given that a : b = p : q
Let a = px, b = qx
a + b = -n/l
⇒ px + qx = -n/l
⇒ (p + q)x = -n/l
⇒p + q = -n/lx .............(2)
Also a*b = n/l
⇒ px * qx = n/l
⇒ pq*x² = n/l
⇒ √pq * x = √(n/l)
⇒ √pq = √(n/l)/x ..........(3)
Now from equation 1, 
    (-n/lx)/(√(n/l)/x) + √(n/l)
= (-n/l)/(√(n/l)) + √(n/l)
= -√(n/l) + √(n/l)
= 0
So, √(p/q) + √(q/p) + √(n/l) = 0
 
3 months ago
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