if-a-lt-b-show-that-a-lt-mb-na-m-n-lt-b-a-b-m-n-are-arbitrary-constants-

Question Number 170838 by pablo1234523 last updated on 01/Jun/22

if a < b, show that a < \frac{m b + n a}{m + n} < b

a, b, m, n are arbitrary constants

Answered by chengulapetrom last updated on 04/Jun/22

if a < b, show that a < \frac{m b + n a}{m + n} < b

a, b, m, n are arbitrary constants

n a < n b

m a < m b

n a + m a < m b + n a

a (m + n) < m b + n a

a < \frac{m b + n a}{m + n} \dots \dots \dots \dots . (i)

n a + m b < n b + m b

m b + n a < b (m + n)

\frac{m b + n a}{m + n} < b \dots \dots \dots \dots \dots (i i)

c o m b i n i n g (i) a n d (i i) y i e l d s

a < \frac{m b + n a}{m + n} < b

Commented by pablo1234523 last updated on 07/Jun/22

thanks sir .

but if n < 0 then n a > n b

then it will be incorrect