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Equalities 1 (hrmacbeth.github.io)

submitted 2 weeks ago* (last edited 2 weeks ago) by [email protected] to c/[email protected]

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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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[–] [email protected] 4 points 2 weeks 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 ◽