Advertisements
Advertisements
प्रश्न
If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).
Advertisements
उत्तर
b is the mean proportional between a and c then
b2 = ac …(i)
Now if (ab + bc) is the mean proportional
between (a2 + b2) and (b2 + c2), then
(ab + bc)2 = (a2 + b2) (b2 + c2)
Now L.H.S. = (ab + bc)2
= a2b + b2c2 + 2ab2c
= a2(ac) + ac(c)2 + 2a ac.c ...[from (i)]
= ac(a2 + c2 + 2ac)
= ac(a + c)2
R.H.S. = (a2 + b2)(b2 + c2)
= (a2 + ac)(ac + c2) ...[from (i)]
= a(a + c) c(a + c)
= ac(a + c)2
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If p : q = r : s; then show that: mp + nq : q = mr + ns : s.
If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`
Find the fourth proportion to the following:
0.7, 4.9 and 1.6
If a : b = c : d; then show that (ax+ by) : b = (cx+ dy) : d
Find the fourth proportional to `(1)/(3), (1)/(4), (1)/(5)`
Show that the following numbers are in continued proportion:
36, 90, 225
The cost of 18 chairs is Rs 22770. How many such chairs can be bought for Rs 10120?
If 57 : x : : 51 : 85, then the value of x is
If a, b, c are in continued proportion, prove that: abc(a + b + c)3 = (ab + bc + ca)3
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
