Question

find the value of a³+8b³, if a +2b=10 and ab=15

Answer 1

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$\underline{SOLUTION}$ ➡

$\underline{Given \: :} \: \: a + 2b = 10 \: ---->(1)\\ \\ ab = 15 \: ---->(2)\\ \\ \underline{ To \: find \: :} \: \: a {}^{3} + 8 b {}^{3}=?$

$Now, \\ \\ a {}^{2} - a \times 2b + (2b) {}^{2} \\ \\ = a {}^{2} - 2ab + 4b {}^{2} \\ \\ = a {}^{2} - 2ab +4 b {}^{2} + 4ab - 4ab \\ \\ = a {}^{2} + 4ab + 4b {}^{2} - 6ab \\ \\ = ( a + 2b ) {}^{2} - 6ab \\ \\ = (10) {}^{2} - 6 \times 15 \: \: [From \: \: (1) \: and \: (2)]\\ \\ = 100 - 90 \\ \\ = 10 \\ \\So , \\ \\ a {}^{2} - a\times 2 b+ (2b) {}^{2} = 10 \: - - - - > (3)$

$We \: \: know \: \: that\\ \\ \boxed{a{}^{3}+b{}^{3}=(a+b)(a{}^{2}-ab+b{}^{2}}$

$a {}^{3} + (2 b) {}^{3} = (a + 2b)[a {}^{2} - a \times 2b +(2 b) {}^{2} ]\\ \\ = > a {}^{3} + 8b {}^{3} = 10 \times 10 \: \: \:[from \: \: (1) \: and \: (3)]\\ \\ = > a{}^{3} + 8b {}^{3} = 100$

$\underline{ANSWER}$ ➡ $\boxed{a {}^{3} + 8 b {}^{3} = 100}$

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Answer 2

Answer:

100

Step-by-step explanation:

Given: a+2b=10 and ab=15

By using identity (a+b)2=a2+b2+2ab

a2+4b2+4ab=100

a2+4b2=100-4ab

Answer: (a)3+(2b)3

by using identity a3+b3= (a+b)(a2+b2-ab)

(a+2b)(a2+4b2-2ab)

(10)(100-4ab-2(15))

(10)(100-4(15)-30)

(10)(100-60-30)

(10)(10)

100

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