Question

1/x+y-1/2x=1/30 ,5/x+y+1/2x=4/3. hence find the value of 2xsquare-ysquare​

Answer 1

Answer:

2x^2-y^2= -15.14

Step-by-step explanation:

(1/x+y)-(1/2x)=(1/30)

(5/x+y)+(1/2x)=(4/3)

Let (1/x+y)=p and (1/2x)=q

p-q=(1/30)

30p-30q-1=0 [By Cross Multiplying]-------------(1)

Similarly,

5p+q=(4/3)

15p+3q-4=0 [By cross Multiplying]---------------(2)

By Elimination Method, multiplying 2 in equ.(2)

30p+6q-8=0----------------------------------------------(3)

Now by Subtracting equ.(1) to equ.(3), we get

        30p-30q-1=0

    -

        30p+6q-8=0

     -         -    +

   -----------------------

        0  -36q +7=0

            -36q= -7

                 q= -7/-36

                 q=7/36

Now putting the value of q in equ.(2),

15p+3q-4=0

15p+(3*7/36)-4=0

15p+(7/12)-4=0

(180p+7-48)/12=0

180p+7-48=0*12

180p-41=0

    180p=41

          p=41/180

Now,

(1/x+y)=p

(1/x+y)=(41/180)

180=41x+41y [By Cross Multiplying]--------------(4)

(1/2x)=q

(1/2x)=7/36

   36= 14x

     x= 36/14

     x= 18/7

Now, putting the value of x in equ.(4)

41x+41y-180=0

41*(18/7)+14y-180=0

(738/7)+14y-180=0

(738+98y-1260)/7=0

98y-1260+738=0*7

98y-522=0

98y= 522

    y= 522/98

    y=261/49

Now, putting the value of x&y in 2x^2+y^2

=>2x^2+y^2

=>2*(18/7)^2-(261/49)^2

=>2*(324/49)-(68121/2401)

=>(648/49)-(68121/2401)

=>(31752-68121)/2401

=> (-36369)/2401

=> -15.14

Hence, the value of 2x^2+y^2 is -15.14

HOPE IT HELPS (n_n)