Q:-solve this and then find pq
____________
Answers
Answer:
Q:-solve this and then find pq
{a}^{4} + {b}^{4} = ( {a}^{2} + pab + {b}^{2} )( {a}^{2} - qab + {b}^{2} )a
4
+b
4
=(a
2
+pab+b
2
)(a
2
−qab+b
2
)
\huge\tt\underline\blue{Answer }
Answer
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⟹ {a}^{4} + {b}^{4} = { ({a}^{2} )}^{2} + {( {b}^{2} )}^{2}⟹a
4
+b
4
=(a
2
)
2
+(b
2
)
2
⟹ {( {a}^{2} + {b}^{2} ) }^{2} - 4 {a}^{2} {b}^{2} [tex]⟹ { ({a}^{2} + {b}^{2} )}^{2} - ( {2ab)}^{2}⟹(a
2
+b
2
)
2
−4a
2
b
2
[tex]⟹(a
2
+b
2
)
2
−(2ab)
2
⟹ {a}^{4} + {b}^{4} = ( {a}^{2} + {b}^{2} + 2ab)( {a}^{2} + {b}^{2} - 2ab)⟹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} )⟹(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∴pq=2x
2
=4
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HOPE IT HELPS YOU..
_____________________
Thankyou:)
Answer:
a⁴- b⁴ = (a²)² - (b²)² = (a² + b²)(a² - b²) = (a² + b²)(a + b)(a b); three factors.
a⁴-b⁴ = ((a+b?)(a+b)(a-b) = (a? + ab(a+b)+ b°{a-b); two factors.
a*-b* = ((a+b°(a-b){a+b) = {a-ab(a-b)-6)
(a+b); two factors.