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Find the square root of (4a + 5b + 5c)^(...

Find the square root of `(4a + 5b + 5c)^(2) - (5a + 4b + 4c)^(2) + 9a^(2)`

A

`sqrt3 (b +c)`

B

`3(b +c -a)`

C

`3(b +c )`

D

`3( b + c -a)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(4a +5b + 5c)^(2) - (5a + 4b + 4c)^(2) + 9a^(2)`
`= (4a + 5b + 5c + 5a + 4b + 4c) (4a + 5b + 5c -5a - 4b -4c) + 9a^(2)`
`= (9a + 9b + 9c) (-a +b +c) + 9a^(2)`
`= 9 (a +b +c) (-a + b +c) = 9a^(2)`
`= 9 (b + c)^(2) -9a^(2) + 9a^(2)`
`= 9 (b +c)^(2)`
`:.` The square root of the given expression is `sqrt(9(b+c)^(2)) = 3(b +c)`
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