Advertisements
Advertisements
Question
If a,b,c are in continued proportion,
show that: `("a"^2 + "b"^2)/("b"("a" + "c")` = `("b"("a" + "c"))/("b"^2 + "c"^2)`
Advertisements
Solution
Sine a, b, c are in continued proportion,
`"a"/"b" = "b"/"c"`
⇒ b2 = ac
Now, (a2 + b2)(b2 + c2) = (a2 + ac)(ac + c2)
= a(a + c) c(a + c)
= ac( a + c)2
= b2 ( a + c)2
⇒ (a2 + b2)(b2+ c2) = [b(a + c)] [b(a + c)]
⇒ `("a"^2+"b"^2)/("b"("a"+"c")` = `("b"("a"+"c"))/("b"^2+"c"^2)`
RELATED QUESTIONS
If r2 = pq, show that p : q is the duplicate ratio of (p + r) : (q + r).
A man's monthly inoome is Rs 5,000. He saves every month a minimum of R~ 800. Find the ratio of his:
monthly savings to monthly expenses.
Find the duplicate ratio of the following :
`2/3 : 4/9`
The present age of two persons are in the ratio 4: 3. Nine years hence their ages will be in the ratio 23: 18. Find their present ages.
Find: The sub-triplicate ratio of 216: 343
Find the sub-triplicate ratio of 1 : 216
Find the following ratio in the simplest form:
24 to 56
10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?
There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.
Mother wants to divide Rs 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.
