1.

The -number of solutions of the equation `cos(pisqrt(x-4)cos(pi sqrtx)=1` is

Answer» We have
`cos(pi sqrt(x)) cos (pi sqrt(x-4))=1`, where `x ge 4`
`rArr cos (pi sqrt(x))=1` and `cos (pisqrt(x-4))=1`
`rArr pisqrt(x)=2m pi` and `(pi sqrt(x-4))=2n pi" "(m, n in Z)`
`rArr x=4 m^(2) and x-4=4n^(2)`
Now, `m^(2)-n^(2)=1`
`rArr m=1, n=0`
`:. x=4`
So, `x=4` is the only solution of the equation.


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