Question

If 3x + 4y = 18 and xy =6, find the value of 9x + 16y.

Answer 1

3x+4y = 18
squaring on both sides
(3x+4y)^2= (18)^2
(3x)^2+(4y)^2+ 2(3x)(4y) = 324
9x^2+ 16y^2+ 24xy = 324
now put xy = 6
9x^2+ 16y^2+24(6)= 324
9x^2+16y^2 + 144= 324
9x^2+ 16 y^2 = 324-144
9x^2+ 16y^2 = 180 ans

Answer 2

Answer:

180

Step-by-step explanation:

We have,

3

x

+

4

y

=

18

on Squaring on both sides, we get

⇒

(

3

x

+

4

y

)

2

=

324

⇒

(

3

x

)

2

+

(

4

y

)

2

+

24

x

y

=

324

We have,

x

y

=

6

⇒

9

x

2

+

16

y

2

+

24

×

6

=

324

⇒

9

x

2

+

16

y

2

+

144

=

324

∴

9

x

2

+

16

y

2

=

180