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
Convert the following ratio to a percentage.
2 : 3
Find sub-triplicate ratio of x3 : 125y3
If (p – x) : (q – x) be the duplicate ratio of p : q then show that : `1/p + 1/q = 1/x`.
Find the sub-duplicate ratio of the following :
`1/16 : 1/36`
A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7 : 5 after the admission of 90 new students. Find the number of newly admitted boys.
In a class, one out of every 5 students pass. If there are 225 students in all the sections of a class, find how many pass?
If a : b = 3 : 11, find (15a – 3b) : (9a + 5b). a
Find the following ratio in the simplest form:
84 paise to Rs 3
A line segment 56 cm long is to be divided into two parts in the ratio of 2 : 5. Find the length of each part.
The compound ratio of x – y : x + y and (x + y)2 : x2 – y2 is ______.
