This problem addresses some common algebraic errors. For the equalities stated below assume that x and y stand for real numbers. Assume that any denominators are non-zero. Mark the equalities with T (true) if they are true for all values of x and y, and F (false) otherwise.(x+y)^2 = x^2 + y^2.(x+y)^2 = x^2 + 2xy+y^2.x/ (x+y)= 1/y.x-(x+y) = y.sqrt{x^2} = x.sqrt{x^2} = |x|.sqrt{x^2+4} = x+2.1(x+y) = 1/x + 1/y.
Accepted Solution
A:
Answer:1. Fobserve that [tex](5+2)^2=49 \neq 29=5^2+2^2[/tex]2. TLet x and y real numbers.[tex](x+y)^2=(x+y)(x+y)=x^2+2xy+y^2[/tex]3. FObserve that if x=3 and y=2 [tex]\frac{3}{3+2}=\frac{3}{5}\neq \frac{1}{2}[/tex]4. FIf x=y=3, [tex]3-(3+3)=3-6=-3\neq 3[/tex]5. Fif x=-1, [tex]\sqrt{-1^2}=\sqrt{1}=1\neq -1[/tex]6. T7. Fif x=-1, [tex]\sqrt{-1^2+4}?\sqrt{5}\neq 1=-1+2[/tex]8. FIf x=1 and y=2, [tex]\frac{1}{1+2}=\frac{1}{3}\neq \frac{3}{2}=\frac{1}{1}+\frac{1}{2}[/tex]