Question

9 X square + 16 Y squared equals to 60 and 3 X + 4 Y = to 6 then find the value of x y

Answer 1

Hey


Given :-

♦ 9x² + 16y² = 60 –––( i )

♦ 3x + 4y = 6 –––( ii )


To find :- Value of x any y .

Now ,


3x + 4y = 6

=> 3x = 6 - 4y

=> x = 6 - 4y / 3

Now putting value of x in eq( i )

we get ,

9x² + 16y² = 60


=> 9 ( 6 - 4y / 3 ) ² + 16y² = 60


=> 9 ( 6 - 4y² ) / 9 + 16 y² = 60


=> 36 + 16y² - 48y + 16y² = 60


=> 32y² - 48y - 24 = 0


=> 4y² - 6y - 3 = 0


D = ( - 6 ) ² - 4 ( 4 ) ( -3 )

= 36 + 48

= 84

= 2√21

So ,

y = 6 + 2√21 / 2

y = 2 ( 3 + √21 ) / 2

y = 3 + √21


And ,


y = 3 - √21 .


So ,

x = 6 - 4y / 3

= 6 - 4 ( 3 + √21 ) / 3

= 6 - 12 - 4√21 / 3

= -6 -4√21 / 3

= -2 ( 3 + 2√21 ) / 3 .


Or ,

x = 6 - 4 ( 3 - √21 ) / 3

= 6 - 12 + 4√21 / 3

= 4√21 - 6 / 3

= 2 ( 2√21 - 3 ) / 3 .




thanks :)