Question

please give the answer for 29 question

Answer 1

xy=4
y=4/x
2x+y=6
2x+4/x=6
2x2+4=6x
2x2-6x+4=0
2x2-4x-2x+4=0
2x (x-2)-2 (x-2)=0
x=2,1
if x=2 then y=2-------2x-y=2
if x=1 then y=4--------2x-y=-2

Answer 2

If 2x+y=6 then,

         y=6-2x,.......(i)

using (i) in xy

=>   xy=4

     x(6-2x)=4

     6x-2x^2=4

    -2x^2+6x=4

    -2x^2+6x-4=0                

    2x^2-6x+4=0                  (multiplied by -(minus))

      x^2-3x+2=0

      x^2-2x-x+2=0

      x(x-2)-1(x-2)=0

      (x-1)(x-2)=0

     x-1=0 or x-2=0

     x=1 or x=2

if x=1 then
   
2x+y=6

2(1)+y=6

2+y=6

y=6-2=4

y=4 ,

2x-y = 2(1)-4=2-4=-2

when x=2

2x+y=6

2(2)+y=6

4+y=6

y=6-4

y=2

then, 2x-y=2(2)-2=4-2=2

aliter,

2x+y=6

as,we know (a+b)^2=a^2+2ab+b^2, using this we square both the sides

(2x+y)^2=(6)^2             

(2x)^2+(y)^2+2(2x)(y)= (6)(6)

4x^2+y^2+4xy=36

4x^2+y^2+4(4)=36

4x^2+y^2+16=36

4x^2+y^2 =36-16

4x^2+y^2=20 ......(i)

we are going to apply (a-b)^2=a^2+b^2-2ab here,

  (2x-y)^2

=(2x)^2+(y)^2-2(2x)(y)

=4x^2+y^2-4xy

=(4x^2+y^2)-4(xy)

=20-4(4)=20-16

(2x-y)^2=4

2x-y=√4

2x-y=2 (or) 2x-y=-2