Question

If a-b=8 and ab=5 then find the value of a3-b3

Answer 1

• Given

• a - b = 8
• ab = 5

• To find

• Value of $a^3 - b^3$

• Solution

Identity to be used -

$\underline{\boxed{\sf{(a - b)^3 = a^3 - b^3 - 3ab}}}$

Substitute the given values.

⇛ $\sf{(8)^3 = a^3 - b^3 - 3 \times 5}$

⇛ $\sf{512 = a^3 - b^3 - 15}$

⇛ $\sf{512 + 15 = a^3 - b^3}$

⇛ $\sf{a^3 - b^3 = 527}$

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Verification

⇛$\sf{(a - b)^3 = a^3 - b^3 - 3ab}$

⇛$\sf{(a - b)^3 = 527 - 3 \times 5}$

⇛$\sf{(a - b)^3 = 527 - 15}$

⇛$\sf{(a - b)^3 = 512}$

⇛ $\sf{(a - b) = 8}$

Hence, verified.

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Know more -

Some useful identities -

• $\sf{{(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}$

• $\sf{{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$

• $\sf{(a + b)^3 = a^3 + b^3 + 3ab(a + b)}$

Signs are changed on the following bases -

• (-) (-) = (+)

• (+) (+) = (+)

• (-) (+) = (-)

• (+) (-) = (-)

Answer 2

$\sf Given \begin{cases} & \sf{a - b =8} \\ & \sf{ab = 5} \end{cases}$

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To find : Value of $\sf{a^3 - b^3}$ ?

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⠀⠀━━━━━━━━━━━━━━━━━━━━━

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\sf{\pink{(a - b)^3 = a^3 - b^3 - 3ab}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

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$:\implies\sf (8)^3 = a^3 - b^3 - 3 \times 5$

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$:\implies\sf 512 = a^3 - b^3 - 15$

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$:\implies\sf 512 + 15 = a^3 - b^3$

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$:\implies\sf 512 + 15 = a^3 - b^3$

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$:\implies{\underline{\boxed{\frak{\purple{a^3 - b^3 = 527}}}}}\;\bigstar$

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$\therefore\:{\underline{\sf{The\:value\:of\:a^3-b^3\:is\: {\textsf{\textbf{527}}}.}}}$