Find the roots of the following equations:
(i) $\quad x-\frac{1}{x}=3, x \neq 0$
(ii) $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x \neq-4,7$

Answer

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Video Transcript

in the solution we have to find the root of the following question. So here in part X negative one upon X equal to three where acts is not equal to zero. So now we can simplify the situation. So here we get access square negative one upon X equal to three. So now we multiply both sides by X. So here we get access square negative one equal to three X. You can write like that. Access choir negative three X negative one equal to zero. So now we compared to your question eight times X squared plus bx plus equal to zero. So now here we have equal to one be equal to negative three and C equal to negative one on comparing to the quarry question. So now here we know that quadratic formula X equal to now it will be plus minus squared off be square negative four times a C upon two times A. So now we apply that formula here so X equal to negative negative three plus minus. scrabbled off be square. So here negatory to the power to negative four times A. Which is the value of one time. See this is the value of negative one upon do that one. So now we simplify this. So here we get X equals negative times negative equal to positive. So positive three plus minus square it off nine positive for upon to sooner here we get X equal to three plus minus described of 13 upon to so we get aks equal to three plus crowd or 13 up on two and X equal to three plus. Sorry, negative square 13 upon tooth. That is the root of that question. So it is our answer for particles. No one point expose for 91 of xnegative equal 11.30 where act is not equal to negative four and seven. So here, first of all we make like denominator. So here we get X close four times xnegative seven in new minute. Or we get X negative seven negative xnegative full equal to 11 up on 30. So now here we simplify this and here we get 11 upon X squared negative Korea 1928 equal to 11 upon 30. Now we do divide both sides by 11. So here we get 91 upon ax squared 92 3 X negative 28 equal to 11 upon 30 sorry one upon 30. Now here we do cross multiply. So here we get access square negative three X negative 28 equal to nine or 30. Now we had 32 the both sides. So here we get axis square 92 3 X positive to equal to see you. So here in northern a time access square blows be times X plus C equal to zero. That is a general court in question. Now we're comparing this so here the hell equal to one equal to 93 and sequel to two. So we apply Kordic Pamela which is X equal to negative B plus minus square root. We square negative for a C upon two times A. So now here we put the value of A B. C. So we get X equal to 92 93 plus minus is quite at all negative three to the power to negative four times one times two upon to A. So here the value of A is one. So we uh put here two times one. So now here we simplify this and we get three plus minus squared off one upon do so here either X equals two, three plus one upon to equal to do oh all X equal to three negative one upon to equal to one. So here, rules of co regulation is X equal to one, oh X equal to two, so it is our final answer for.

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