Advertisements
Advertisements
Question
If `"a"/("b + c") = "b"/("c + a") = "c"/("a + b")` , then prove that a(b - c) + b(c-a) + c (a - b) = 0
Advertisements
Solution
`"a"/("b + c") = "b"/("c + a") = "c"/("a + b") = "k"`
a = k(b + c)
b = k(c+a)
c= k(a+b)
a (b - c)+ b (c - a)+ c (a - b) = 0
LHS
a (b - c)+ b (c - a)+ c (a - b)
= k (b + c )(b - c) + k ( c + a)( c - a) + k (a + b )(a - b)
= k(b2 - C2) + k( c2 - a2) + k( a2 - b2)
= kb2 - kc2 + kc2 - ka2 + ka2 - kb2
= 0 = RHS
LHS = RHS. Hence, proved.
APPEARS IN
RELATED QUESTIONS
If 15(2x2 – y2) = 7xy, find x : y; if x and y both are positive.
Find the duplicate ratio of the following :
`3 sqrt (2"a") : 2 sqrt (3"a")`
Express the following ratios in its simplest form :
200:250
If a : b = 5 : 3, show that (5a + 8b) : (6a – 7b) = 49 : 9.
The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg; find the weight of copper in the alloy.
Find the duplicate ratio of 2 : 3
If (x + 2y) : (2x – y) is equal to the duplicate ratio of 3 : 2, find x : y.
Express the following ratio in the simplest form:
36 : 90
See the figure and find the ratio of number of squares to all the figures inside the rectangle.
Two numbers are in the ratio 5 : 8. If 10 is subtracted from each number, the ratio becomes 4 : 7. The numbers are ______.
