Math, asked by Anonymous, 6 months ago

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

Answers

Answered by Anonymous
10

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Q:-solve this

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

\huge\tt\underline\blue{Answer }

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

⟹ {( {a}^{2} +  {b}^{2} ) }^{2}  - 4 {a}^{2}  {b}^{2} </strong></p><p></p><p><strong>[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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HOPE IT HELPS YOU..

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Thankyou:)

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