1. Proofs by calculation — The Mechanics of Proof, by Heather Macbeth
hrmacbeth.github.io

Let a and b be rational numbers and suppose that (a-b)=4 and a*b=1 . Show that (a+b)^2 = 20.

  • scratsearcher 🔍🔮📊🎲OPEnglish
    4·
    7 days ago
    hint

    Use algebraic substitution and the binomial formulas

    (a+b)^2 = a^2+2*ab+b^2

    (a-b)^2 = a^2-2*ab+b^2
    Solution 
    (a+b)^2 = a^2 + 2*ab + b^2 = (a-b)^2 +4*ab = 4^2+4*1 = 16+4 = 20 ◽