Question

Simplify: √x2-y2-y÷x-√x2-y2 + √x2-y2+x÷√x2-y2+y

Answer 1

Answer:

( X + Y ) ^2 = ( X + Y ) ( X + Y ) = X ( X +Y ) + Y ( X + Y ) = X^2 + 2X Y + Y ^2

X + Y = √( X + Y ) ^2 = √( X^2 + 2XY + Y ^2 ) ≠ √( X^2 + Y^2)

By Pythagoras Theorem:

X^2 + Y ^2 = Z ^2 / Z is the hypotenuse of a right triangle with X , Y as legs

Z = √(X ^ 2 + Y ^2)

If letting √( X^2 + Y ^2 ) equals X +y is in violation of Pythagoras theorem with implication that

length of the hypotenuse equals the Sum of the length of the legs, rather than square of the

hypotenuse being equal the Sum of the square of 2 length.

One Simple counter example defies that .

let X = 3 Y = 4

√(X^2 + Y ^2) = √ (3^2 + 4 ^2) = √25 =5

( √X ^2 )+( √Y ^2 ) = X + Y = 4 +3 =7

Students should remember that They can multiply and divide Radicals. but can not add or subtract.