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

Step-by-step explanation:

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-solve this and then find pq

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

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

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

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

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

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

On comparing both sides :-

we get p=2 & q =2

$∴pq = 2 {x}^{2} = 4$

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HOPE IT HELPS YOU..

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Thankyou:)

Answer 2

Answer:

Given,

Area of rectangle = 25x2 – 35x + 12

We know, area of rectangle = length × breadth

So, by factoring 25x2 – 35x + 12, the length and breadth can be obtained.

25x2 – 35x + 12 = 25x2 – 15x – 20x + 12

=> 25x2 – 35x + 12 = 5x(5x – 3) – 4(5x – 3)

=> 25x2 – 35x + 12 = (5x – 3)(5x – 4)

So, the length and breadth are (5x – 3)(5x – 4).

Now, perimeter = 2(length + breadth)

So, perimeter of the rectangle = 2[(5x – 3)+(5x – 4)]

= 2(5x – 3 + 5x – 4) = 2(10x – 7) = 20x – 14

So, the perimeter = 20x – 14