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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

```							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 : qLet a = px, b = qxa + 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)= 0So, √(p/q) + √(q/p) + √(n/l) = 0
```
3 months ago
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