Question

If 5x - 2y = 7 and xy = -1,
Find the value of
${9x}^{2} + {16y}^{2}$
First correct answer will be marked as brainliest...!!,

Answer 1

                                  ________________


Given,

5x - 2y = 7  -------- ( 1 )

 xy = -1

∴  y = -1/x.  ------ ( 2 )

By substituting the value of y in ( 1 ),

⇒ 5x - 2 ( -1/x ) = 7

⇒ 5x + ( 2/x ) = 7

⇒ ( 5x² + 2 ) / x = 7

⇒ 5x² + 2 = 7x

⇒ 5x² - 7x + 2 = 0

⇒ 5x² - 5x - 2x + 2 = 0

⇒ 5x ( x - 1 ) - 2 ( x - 1 ) = 0

⇒ ( x - 1 ) ( 5x - 2 ) = 0

∴ x = 1 or ( 2/5 ) = 0.4

By substituting x = 1 in ( 1 )

⇒ 5x - 2y = 7

⇒ 5(1 ) - 2y = 7

⇒ 5 - 2y = 7

⇒ -2y = 7 - 5

⇒ -2y = 2

⇒ y = 2/-2

∴  y = -1

Now,

= 9x² + 16y²

= 9 ( 1 )² + 16 ( -1 )²

= 9 (1 ) + 16(1)

= 9 + 16

= 25.

By substituting x = 0.4 in ( 1 ),

⇒ 5x - 2y = 7

⇒ 5 ( 0.4 ) - 2y = 7

⇒ 2 - 2y = 7

⇒ -2y = 7 -2

⇒ -2y = 5

⇒ y = 5 / ( -2 )

∴ y = -2.5

Now,

= 9x² + 16y²

= 9 ( 0.4 )² + 16 ( -2.5 )²

= 9 ( 0.16 ) + 16 ( 6.25 )

= 1.44 + 100

= 101.44


So, answers = 25 or 101.44

Answer 2

                                  ________________

Given,

5x - 2y = 7  -------- ( 1 )

 xy = -1

∴  y = -1/x.  ------ ( 2 )

By substituting the value of y in ( 1 ),

⇒ 5x - 2 ( -1/x ) = 7

⇒ 5x + ( 2/x ) = 7

⇒ ( 5x² + 2 ) / x = 7

⇒ 5x² + 2 = 7x

⇒ 5x² - 7x + 2 = 0

⇒ 5x² - 5x - 2x + 2 = 0

⇒ 5x ( x - 1 ) - 2 ( x - 1 ) = 0

⇒ ( x - 1 ) ( 5x - 2 ) = 0

∴ x = 1 or ( 2/5 ) = 0.4

By substituting x = 1 in ( 1 )

⇒ 5x - 2y = 7

⇒ 5(1 ) - 2y = 7

⇒ 5 - 2y = 7

⇒ -2y = 7 - 5

⇒ -2y = 2

⇒ y = 2/-2

∴  y = -1

Now,

= 9x² + 16y²

= 9 ( 1 )² + 16 ( -1 )²

= 9 (1 ) + 16(1)

= 9 + 16

= 25.

By substituting x = 0.4 in ( 1 ),

⇒ 5x - 2y = 7

⇒ 5 ( 0.4 ) - 2y = 7

⇒ 2 - 2y = 7

⇒ -2y = 7 -2

⇒ -2y = 5

⇒ y = 5 / ( -2 )

∴ y = -2.5

Now,

= 9x² + 16y²

= 9 ( 0.4 )² + 16 ( -2.5 )²

= 9 ( 0.16 ) + 16 ( 6.25 )

= 1.44 + 100

= 101.44

So, answers = 25 or 101.44