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