1.

 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.

As x must be real, the discriminant must be ≥0

Make discriminant D ≥ 0

After solving the discriminant equation you will get the number of integral solution.



Discussion

No Comment Found