InterviewSolution
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InterviewSolution
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Solve the equation `sqrt((6-4x-x^(2)))=x+4` |
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Answer» We have `sqrt((6-4x-x^(2)))=x+4` This equation is equivalent to the system `{(x+4ge0),(6-4x-x^(2)=(x+4)^(2)):}` `implies{(xge-4),(x^(2)+6x+5=0):}` On solving the equation `x^(2)+6x+5=0` We find that `x_(1)=(-1)` and `x_(2)=(-5)` only `x_(1)=(-1)` satisfies the condition `xge-4`. Consequently the number `-1` is the only solution of the given equation. Form 3 An equation in the form `root(3)(f(x))+root(3)(g(x))=h(x)` .........i where `f(x),g(x)` are the functions of `x` but `h(x)` is a function of `x` or constant, can be solved as follows cubing both sides of the equation we obtain `f(x)+g(x)=3root(3)((f(x)(g))(root(3)(f(x))+root(3)(g(x)))=h^(3)(x)` `impliesf(x)+g(x)+3root(3)(f(x)g(x))(h(x))=h^(3)(x)` [from Eq. (i)] We find its roots and then substituting then into the original equation, we choose those which are the roots of the original equation. |
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