0

Guest

Courses New

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

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
 

Grade:

1 Answers

Arun
25750 Points
4 years ago
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
 

Think You Can Provide A Better Answer ?

Other Related Questions on Discuss with colleagues and IITians

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More