

InterviewSolution
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Answer the question in the given image. Find the number of integral solution of the equation 7(y+1/y)-2(y2+1/y2)=9 |
Answer» We know that (a+b)2=a2+b2+2ab take a=y, and b=1/y a2+b2=(a+b)2-2ab y2+1/y2=(y+1/y)2-2x y x 1/y y2+1/y2 =(y+1/y)2-2..........................(1) 7(y+1/y)-2(y2+1/y2)=9 7(y+1/y)-2[(y+1/y)2-2]=9..............from equation(1) taking (y+1/y)=z we get 7z-2[z2-2]=9 => 7z-2z2+4=9 => -2z2+7z-5=0................(2) solving equation (2) we get 2z2-7z+5=0 => z(2z-5)-1(2z-5)=0 => (z-1)(2z-5)=0 =>(z-1)=0 or (2z-5)=0 z=1 or, z=5/2 Now, y+1/y=1 or y+1/y=5/2 => y2+1=y => y2-y+1=0 [this is not possible] Now, y+1/y=5/2 =>y2+1=5y/2 => 2y2+2=5y => 2y2-5y+2=0 =>2y(y-2)-1(y-2)=0 => (2y-1)(y-2)=0 =>2y-1=0 ,y-2=0 number of integral solution of the equation y=1/2, y=2 Arrange the equation in quadratic form. |
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