Advertisements
Advertisements
प्रश्न
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
Advertisements
उत्तर
Let the required third proportional be p.
`=> x/y + y/x, sqrt(x^2 + y^2)`, p are in continued proportion
`=> x/y + y/x : sqrt(x^2 + y^2) = sqrt(x^2 + y^2) : p`
`=> p(x/y + y/x) = (sqrt(x^2 + y^2))^2`
`=> p((x^2 + y^2)/(xy)) = x^2 + y^2`
`=>` p = xy
संबंधित प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx2 – 2ax + 3b = 0.
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
If a, b, c are in continued proportion and a(b – c) = 2b, prove that: `a - c = (2(a + b))/a`.
If 9 kg of rice costs Rs 327.60, what will be the cost of 50 kg of rice?
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
If Rs 760 is divided between A and B in the ratio 8 : 11, then B's share is
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not
