Advertisements
Advertisements
प्रश्न
If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.
Advertisements
उत्तर
Since, q is the mean proportional of p and r.
Hence, q2 = pr.
R.H.S. = `q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`
= `q^4[(1)/p^2 - (1)/(pr) + (1)/r^2]`
= `q^4[(r^2 - pr + p^2)/(p^2r^2)]`
= `q^4[(p^2 - pr + r^2)/(pr)^2]`
= `q^4[(p^2 - pr + r^2)/q^4]`
= p2 - pr + r2
= p2 - q2 + r2 = L.H.S.
Hence proved.
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?
Find the third proportion to the following :
16x2 and 24x
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
If a, 12, 16 and b are in continued proportion find a and b.
If 2x – 1, 5x – 6, 6x + 2 and 15x – 9 are in proportion, find the value of x.
Verify the following:
91 : 104 : : 119 : 136
Write (T) for true and (F) for false in case of the following:
36 : 45 : : 80 : 100
If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and ₹ 4 : ₹ 50
If x, y and z are in continued proportion, Prove that:
`x/(y^2.z^2) + y/(z^2.x^2) + z/(x^2.y^2) = 1/x^3 + 1/y^3 + 1/z^3`
