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Equalities 1 (hrmacbeth.github.io)

submitted 1 month ago* (last edited 1 month ago) by glowing_hans@sopuli.xyz to c/dailymaths@lemmy.world

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

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[–] glowing_hans@sopuli.xyz 4 points 1 month 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 ◽