Question

if a =3+2√2 and b=1\a
find a^4+b^4​

Answer 1

2+2+2=1
a
2
+
b
2


Hope it helps you
+
2
a
b
=
1

Subtracting the second equation from this:

2+2+2−(2+2)=1−2
a
2
+
b
2
+
2
a
b
−
(
a
2
+
b
2
)
=
1
−
2

2=−1
2
a
b
=
−
1

No square that:

422=1
4
a
2
b
2
=
1

222=12
2
a
2
b
2
=
1
2

Squaring 2+2=2
a
2
+
b
2
=
2

4+4+222=4
a
4
+
b
4
+
2
a
2
b
2
=
4

But we already figured out that 222=12
2
a
2
b
2
=
1
2
! So:

4+4+12=4
a
4
+
b
4
+
1
2
=
4

4+4=3.5
a
4
+
b
4
=
3.5

And we have our answer!