Advertisements
Advertisements
Question
If `a/c = c/d = c/f` prove that : `(a^3 + c^3)^2/(b^3 + d^3)^2 = e^6/f^6`
Solution
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S. `(a^3 + c^3)^2/(b^3 + d^3)^2`
= `(b^3k^3 + d^3k^3)^2/(b^3 + d^3)^2`
= `[k^3(b^3 + d^3)]^2/(b^3 + a^3)^2`
= `(k^6(b^3 + d^3)^2)/(b^3 + d^3)^2` = k6
R.H.S. = `e^6/f^6`
= `f^6k^6/f^6` = k6
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
If a, b, c, d are in continued proportion, prove that:
(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2.
Verify the following:
108 : 72 : : 129 : 86
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
Find the value of x if 5 : 3 : : x : 6.
If 22.5 m of a uniform iron rod weighs 85.5 kg, what will be the weight of 5 m of the same rod?
If a, b, c and d are in proportion, prove that: `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`
Determine if the following are in proportion.
15, 45, 40, 120
Are the following statements true?
7.5 litres : 15 litres = 5 kg : 10 kg
If x, 2, 10 and y are in continued proportion, the values of x and y are respectively:
