Question

The product (8+3√2)(8-3√2) is

Answer 1

Step-by-step explanation:

We have,

3

8+x

+

3

8−x

=1...(1)

Let u=

3

8+x

⇒u

3

=8+x

⇒x=u

3

−8...(2)

So, (1) becomes

u+

3

8−(u

3

−8)

=1

⇒

3

8−(u

3

−8)

=1−u

Cubing both sides, we get

8−(u

3

−8)=(1−u)

3

⇒16−u

3

=1−u

3

−3u+3u

2

⇒3u

2

−3u−15=0

⇒u

2

−u−5=0

⇒u=

2(1)

−(−1)±

(−1)

2

−4(1)(−5)

⇒u=

2

1±

21

Put the value of u in (2), we get

x=(

2

1±

21

)

3

−8

⇒x=

8

1±21

21

±3

21

+63

−8

⇒x=

8

1±24

21

+63−64

⇒x=±3

21

∴ roots of the given equation are 3

21

and −3

21

.

And, hence product of roots =3

21

×(−3

21

)=−189