Question

a^4+b^4=(a^2+pab+b^2)(a^2-qab+b^2)then pq=

Answer 1

Answer:

answer for the given problem is given

Answer 2

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Q:-a^4+b^4=(a^2+pab+b^2)(a^2-qab+b^2)then pq=

$\huge\tt\underline\blue{Answer }$

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$⟹</p><p> {a}^{4} + {b}^{4} = ( {a}^{2} + pab + {b}^{2} )( {a}^{2} - qab + {b}^{2} )$

$⟹ </p><p> {a}^{4} + {b}^{4} = { ({a}^{2} )}^{2} + {( {b}^{2} )}^{2}$

$= {( {a}^{2} + {b}^{2}) }^{2} - 4 {a}^{2} {b}^{2}$

$⟹</p><p> { ({a}^{2} + {b}^{2} )}^{2} - {(2ab)}^{2}$

$⟹ {a}^{4} + {b}^{4} = ( {a}^{2} + {b}^{2} + 2ab)( {a}^{2} + {b}^{2} - 2ab)</p><p>$

$⟹( {a}^{2} + 2ab + {b}^{2} )( {a}^{2} - 2ab + {b}^{2} ) = ( {a}^{2} + pab + {b}^{2} )( {a}^{2} - qab + {b}^{2} )</p><p>$

On comparing both sides :-

p=2. , q=2

Therefore,pq=2x^2=4

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HOPE IT HELPS YOU..

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