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InterviewSolution
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The number of solution x of the equation `sin (x+x^(2))- sin(x^(2))= sin x` in the interval [2,3] is |
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Answer» Correct Answer - C `2 cos(x+(2x^(2))/(2)).sin ""(x)/(2)= 2 sin ""(x)/(2). cos ""(x)/(2)` `implies sin ""(x)/(2)[cos((x+2x^(2))/(2))= cos "" (x)/(2)]=0` `sin ""(x)/(2)=0 " " or " "2 sin((2x+2x^(2))/(4)).sin((2x^(2))/(4))=0` `(x)/(2)=0,pi,2pi " "or " "sin((x+x^(2))/(2))=0 " "or" " sin ""(x^(2))/(2)=0` `X=0,2pi,4pi " " or " " (x+x^(2))/(2)=0,pi,2pi` `(x+x^(2))/(2)=pi " " x^(2)=2pi` `implies x^(2)+x-2pi=0" " impliesx=sqrt(2pi)` `x=(-1pmsqrt(1+8pi))/(2)" "2 gtsqrt(2pi) lt3` `sqrt(1+8pi)~~sqrt(25.14)` `" "~~5.2` `:. x=(5.2-1)/(2)=(4.2)/(2)=2.1` `:.` total number of solution lies between (2,3)=2 |
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