Question

If a+b=7 and ab=12 then a⁴-b⁴ = ?​

Answer 1

Answer:

175

Step-by-step explanati

$a + b = 7 \\ squaring \: both \: sides \: \\( a + b) {}^{2} = 49 </p><p>(eq \: 1)\\ {a}^{2} + b {}^{2} + 2ab = 49 \\ value \: of \: ab \: is \: given \: i.e. \: 12 \\ {a}^{2} + b {}^{2} + 2 \times 12 = 49 \\ {a}^{2} + b {}^{2} +24 = 49 \\ {a}^{2} + b {}^{2} = 49 - 24 \\ {a}^{2} + b {}^{2} = 25...(eq \: 2) \\ as \: we \: know \: \\ (a + b) {}^{2} - ( a - b) {}^{2} = 4ab \\ therefore \: using \: value \: from \: (eq1) \\ 49 \: - \: (a - b) {}^{2} = 4 \times 12 \\ 49 \: - \: (a - b) {}^{2} = 48 \\ - (a - b) {}^{2} = 48 - 49 \\ - (a - b) {}^{2} = - 1 \\ (a - b) {}^{2} = 1 \\ (a - b) = \sqrt{1} = 1..(eq3)$

$a {}^{4} - b {}^{4} = { ({a}^{2}) }^{2} + { ({b}^{2}) }^{2} \\ using \: identity \: a {}^{2} - b {}^{2} = (a + b)(a - b) \\ {({a}^{2}) }^{2} + { ({b}^{2}) }^{2} \\ = ({a}^{2} - {b}^{2} )( {a}^{2} + {b}^{2} ) \\using \: same \: identity \: again \\ (a + b)(a - b)( {a}^{2} + {b}^{2} )$

$using \: values \: from \: eq \: 2 \: and \: 3 \\ (a - b)(a + b)(a {}^{2} + b {}^{2}) \\ (1) \times (7) \times (25) \\ 175$

Answer 2

Answer:a2b2=144

check the attachment

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Step-by-step explanation: