Question

Q:-solve this and then find pq
${a}^{4} + {b}^{4} = ( {a}^{2} + pab + {b}^{2} )( {a}^{2} - qab + {b}^{2} )$

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Answer 1

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Q:-solve this and then find pq

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

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

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

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

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

On comparing both sides :-

we get p=2 & q =2

$∴pq = 2 {x}^{2} = 4$

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Answer 2

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

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

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

$↝( {a}^{2} + 2ab + {b}^{2} )( {a}^{2} - 2ab + {b}^{2} ) = ( {a}^{2} + pab + {b}^{2} )( {a}^{2} - qab + {b}^{2} )$

On comparing both sides :-

we get p=2 & q =2

$∴pq = 2 {x}^{2} = 4$