x+5/y+5=3/5
Make it into x/y
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Answer:
x−y=2
⇒x=y+2 .......(i)
x
5
−y
5
=992
Substituting value of (i) in above equation, we get
(y+2)
5
−y
5
=992
⇒(y+2)
3
(y+2)
2
−y
5
=992
⇒(y
3
+8+6y
2
+12y)(y
2
+4+4y)−y
5
=992
⇒y
5
+10y
4
+40y
3
+80y
2
+80y+32−y
5
=992
⇒10y
4
+40y
3
+80y
2
+80y=960
⇒y
4
+4y
3
+8y
2
+8y−96=0
Solving by hit and trial.
Put y=2
16+32+32+16−96=0
Hence, y−2 is the root of the equation.
⇒(y−2)(y
3
+6y
2
+20y+48)=0
Thus y−2=0
and y
3
+6y
2
+20y+48=0
Put y=−4
−64+96−80+48=0
Hence, y+4 is the root of the equation.
⇒(y+4)(y
2
+2y+12)=0
Thus y+4=0
and y
2
+2y+12=0
Using quadratic formula, we have
y=
2
−2±
4−4(1)(12)
=
2
−2±
−44
y=−1±
−11
...........(iv)
Now from (ii),(iii) and (iv)
y=2,−4,−1±
−11
From (i),
x=y+2
⇒x=4,−2,1±
−11
here is your answer..
hopes it helps you...
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