Let-a-and-b-be-positive-real-numbers-with-a-3-b-3-a-b-and-k-a-2-4b-2-then-1-k-lt-1-2-k-gt-1-3-k-1-4-k-gt-2-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 21311 by Tinkutara last updated on 20/Sep/17

Let a and b be positive real numbers with a^3 + b^3 = a − b, and k = a^2 + 4b^2 , then (1) k < 1 (2) k >1 (3) k = 1 (4) k > 2

$$\mathrm{Let}\:{a}\:\mathrm{and}\:{b}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{with}\:{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:=\:{a}\:−\:{b},\:\mathrm{and}\:{k}\:=\:{a}^{\mathrm{2}} \:+\:\mathrm{4}{b}^{\mathrm{2}} , \\ $$$$\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{k}\:<\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:{k}\:>\mathrm{1} \\ $$$$\left(\mathrm{3}\right)\:{k}\:=\:\mathrm{1} \\ $$$$\left(\mathrm{4}\right)\:{k}\:>\:\mathrm{2} \\ $$

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Let-a-and-b-be-positive-real-numbers-with-a-3-b-3-a-b-and-k-a-2-4b-2-then-1-k-lt-1-2-k-gt-1-3-k-1-4-k-gt-2-

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