Question

If X+y= 48 and xy=200 swhat is the value of x2+y2=?
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Answer 1

Answer:

HEY THERE!

Step-by-step explanation:

xy=200—equation 1

x=200/y

x-y=100—equation 2

putting the value of x in equation 2

=>x-y=100

=>200/y - y=100

=>200-y²/y=100

=>200-y²=100y

=>-y²-100y+200=0

=>y²+100y-200=0(taking — common)

Now,

a=1; b=100; c=-200

Y= {-b+√(b²-4ac)}/2a

= {-100+√(100²-4×1×-200)}/2×1

={-100+√(10000+800)}/2

=(-100+√10800)/2

=(-100+60√3)/2

=20(-5+3√3)/2

=10(-5+3√3)

=+- 30√3–50

So the value of y is +30√3–50 or -30√3-50

Putting the value of y in equation 1

xy=200

x=200/y

x=200/(30√3–50) or 200/(-30√3-50)

=200/2(15√3–25) or 200/2(-15√3–25)

=100/(15√3–25) or 100/(-15√3–25)

So the value of x is 100/(15√3–25) or 100/(-15√3–25)  

ANOTHER METHOD OF SOLVING THIS IS:

xy=200—equation 1

x=200/y

x-y=100—equation 2

putting the value of x in equation 2

=>x-y=100

=>200/y - y=100

=>200-y²/y=100

=>200-y²=100y

=>-y²-100y+200=0

=>y²+100y-200=0(taking — common)

Now,

a=1; b=100; c=-200

Y= {-b+√(b²-4ac)}/2a

= {-100+√(100²-4×1×-200)}/2×1

={-100+√(10000+800)}/2

=(-100+√10800)/2

=(-100+60√3)/2

=20(-5+3√3)/2

=10(-5+3√3)

=+- 30√3–50

So the value of y is +30√3–50 or -30√3-50

Putting the value of y in equation 1

xy=200

x=200/y

x=200/(30√3–50) or 200/(-30√3-50)

=200/2(15√3–25) or 200/2(-15√3–25)

=100/(15√3–25) or 100/(-15√3–25)

So the value of x is 100/(15√3–25) or 100/(-15√3–25)

ANOTHER METHOD TO SOLVE THIS IS :

solve

xy = 200

and x-y = 100

then

x = 200/y

x-y = 100

200/y-y = 100

(200-y^2)/y = 100

200-y^2 = 100*y

y^2–200+100y

y^2+100y-200

quadratic equation formula

Y=1.96

again

x-y = 100

x-1.96 = 100

x = 101.96

514 views

solve

xy = 200

and x-y = 100

then

x = 200/y

x-y = 100

200/y-y = 100

(200-y^2)/y = 100

200-y^2 = 100*y

y^2–200+100y

y^2+100y-200

quadratic equation formula

Y=1.96

again

x-y = 100

x-1.96 = 100

x = 101.96

Answer 2

Answer:

1904

Explanation:

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

Given that,

x + y = 48 and xy = 200

$=> x^2+y^2 = (48)^2-2(200)\\=> x^2+y^2 = 2304 - 400\\=> x^2+y^2 = 1904$