Question

prove that x+y=a+b .

Answer 1

x + y = a + b ax - by = a² - b² Eliminate y Multiply the first equation thru by b bx + by = ab + b² ax - by = a² - b² Now add them vertically: bx + by = ab + b² ax - by = a² - b² then — bx+ax = ab+a² bx + ax = ab + a² Factor out x on the left, factor out a on the right x(b + a) = a(b + a) Divide both sides by (a + b) x(b + a) a(a + b) then = — (a + b) (a + b) Cancel x(b + a) a(a + b) then — (a + b) (a + b) x = a Now eliminate x Multiply the first equation thru by -a -ax - ay = -a² - ab ax - by = a² - b² Now add them vertically: -ax - ay = -a² - ab ax - by = a² - b² then — -ay-by = -ab-b² Multiply thru by -1 ay + by = ab + b² Factor out y on the left, factor out b on the right y(a + b) = b(a + b) Divide both sides by (a + b) y(a + b) b(a + b) then — = — (a + b) (a + b) Cancel y(a + b) b(a + b) then — (a + b) (a + b)
y = b
hope it helps u....

OR

Since R(x, y) is a point on the line segment joining the point, P(a, b) and Q(b, a).

∴ P(a, b), Q(b, a) and R(x, y)are the collinear.

⇒ Area of ΔPQR = 0

Area of triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3)

 

HOPE THESE BOTH THE ANSWERS WILL HELP U...THANKS