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In DeltaABC 2a^2+4b^2+c^2=2ab+2ac then n...

In `DeltaABC` `2a^2+4b^2+c^2=2ab+2ac` then numerical value of `cosB` is

A

0

B

`(1)/(8)`

C

`(3)/(8)`

D

`(7)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
`2a^(2)+4b^(2)+c^(2)=4ab+2ac`
`rArr a^(2)+(2b)^(2)-4ab+a^(2)+c^(2)-2ac=0`
`rArr (a-2b)^(2)+(a-c)^(2)=0`
`rArr a=2b=c`
`cos B=(a^(2)+c^(2)-b^(2))/(2ac)`
`=(c^(2)+c^(2)-((c )/(2))^(2))/(2xxc xxc)=(2c^(2)-(c^(2))/(4))/(2c^(2))`
`rArr cos B=(7)/(8)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 16-Paper - 2 (MATHEMATICS )
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