Advertisements
Advertisements
प्रश्न
If `a/c = c/d = c/f` prove that : (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)2
Advertisements
उत्तर
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e = fk
L.H.S. = (b2 + d2 + f2) (a2 + c2 + e2)
= (b2 + d2 + f2) (b2 k2 + d2 k2 + f2 k2)
= k2 (b2 + d2 + f2) k2 (b2 + d2 + f2)
= k2 (b2 + d2 + f2)2
R.H.S. = (ab + cd + ef)2
= (b. kb + dk. d + fk. f)2
= (kb2 + kd2 + kf2)
= k2 (b2 + d2 + f2)2
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.
If a, b, c are in continued proportion, prove that: `(a + b)/(b + c) = (a^2(b - c))/(b^2(a - b)`.
If a, b, c are in continued proportion, prove that: `(1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)`
If a, b, c, d are in continued proportion, prove that: `((a - b)/c + (a - c)/b)^2 - ((d - b)/c + (d - c)/b)^2 = (a - d)^2 (1/c^2 - 1/b^2)`.
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
A particular high school has 1500 students 50 teachers and 5 administrators. If the school grows to 1800 students and the ratios are maintained, then find the number of teachers and administrators
Find the missing number in the box in the proportion:
`square/18 = 2/9`
