\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}=0

1.	\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}=0
Answer» 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 thata : 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 ab = n/l ⇒px qx = n/l ⇒pqx²= 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

Answer»

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 thata : 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

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