Question

Please solve q 56 ?

Answer 1

option (4) is acceptable

Explanation:

`a+b-c`

`=(sqrta+sqrtb)^2-(sqrtc)^2-2sqrt(ab)`

`=(sqrta+sqrtb+sqrtc)(sqrta+sqrtb-sqrtc)-2sqrt(ab)`

`=(sqrta+sqrtb+sqrtc)(sqrtc-sqrtc)-2sqrt(ab)`

`=(sqrta+sqrtb+sqrtc)xx0-2sqrt(ab)`

`=-2sqrt(ab)<0`

So `a+b-c<0=>a+b < c`
This means sum of the lengths of two sides is less than the third side . This is not possible for any triangle.
Hence formation of triangle is not possible i.e option (4) is acceptable

Answer 2

Option (4) is correct.

Explanation:

Given,

`rarrsqrt(a)+sqrt(b)=sqrtc`

`rarr(sqrt(a)+sqrt(b))^2=(sqrtc)^2`

`rarra+2sqrt(ab)+b=c`

`rarra+b-c=-2sqrt(ab)`

`rarra+b-c<0`

`rarra+b<` `c`

So, no formation of triangle is possible.