Question

10) If x^2 +9y^2 = 9 and xy = 1, find (2x + 6y)^2​

Answer 1

Answer:

We have, 3

sec

2

x−1

9y

2

−6y+2

≤1

⇒3

sec

2

x

y

2

−

3

2

y+

9

2

≤1

⇒3

sec

2

x

(y−

3

1

)

2

+

9

1

≤1

Now, sec

2

x≥1⇒3

sec

2

x

≥3 and

(y−

3

1

)

2

+

9

1

≥

3

1

, So

We must have sec

2

x=1 and, y−

3

1

=0.

⇒x=0,π,2π,3π and y=

3

1

.

∴ There are 4 solutions.

Answer 2

I hope you must have understood.