Advertisements
Advertisements
प्रश्न
If y is the mean proportional between x and z, prove that: `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2)) = y^4`.
Advertisements
उत्तर
Given, y is the mean proportional between x and z.
`=>` y2 = xz
L.H.S = `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2))`
= `(x^2 - y^2 + z^2)/(1/x^2 - 1/y^2 + 1/z^2)`
= `(x^2 - xz + z^2)/(1/x^2 - 1/(xz) + 1/z^2)`
= `(x^2 - xz + z^2)/((z^2 - xz + x^2)/(x^2z^2))`
= x2z2
= (xz)2
= (y2)2 ...(∴ y2 = xz)
= y4
= R.H.S
संबंधित प्रश्न
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
If `a/b = c/d`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`.
If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
Determine if the following numbers are in proportion:
22, 33, 42, 63
A car travels 195 km in 3 hours.
(i) How long will it take to travel 520 km?
(ii) How far will it travel in 7 hours at the same speed?
Fill the boxes using any set of suitable numbers 6 : `square` : : `square` : 15
Determine if the following are in proportion.
4, 6, 8, 12
If x + y + z = 0, the value of `x/(y + z)` is ______.
