Advertisements
Advertisements
प्रश्न
If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x2 + y2 and y2 + z2.
Advertisements
उत्तर
Since y is the mean proportion between x and z
Therefore, y2 = xz
Now, we have to prove that xy + yz is the mean proportional between x2 + y2 and y2 + z2,
i.e., (xy + yz)2 = (x2 + y2)(y2 + z2)
LHS = (xy + yz)2
= [y(x + z)]2
= y2(x + z)2
= xz(x + z)2
RHS = (x2 + y2)(y2 + z2)
= (x2 + xz)(xz + z2)
= x(x + z) z (x + z)
= xz(x + z)2
LHS = RHS
Hence, proved.
संबंधित प्रश्न
Find the third proportional to `2 2/3` and 4
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
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]`.
35 inland letters cost Rs 87.50. How many such letters can we buy for 315?
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles
If b : a = c : d, then a, b, c, d are in proportion.
The quarterly school fee in Kendriya Vidyalaya for Class VI is Rs. 540. What will be the fee for seven months?
