If a+1÷a=1 then (1-a+a^2)(1+a-a^2)=?
Answers
Answer:
0
Step-by-step explanation:
Given---> a + 1/a = 1
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To find --->(1-a+a²) (1+a-a²)=?
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Solution--->ATQ , a + 1/a = 1
-------------- Multiplying whole equation by a => a×a + a×(1/a)=a×1
=> a² + 1 =a
=> a² - a =-1
Now, (1-a+a²)(1+a-a²)
=> (1+a²-a)(1-a²+a)
=> {1+(a²-a)} {1-(a²-a)}
Now putting a²-a=-1 in it
=> {1+(-1)} {1-(-1)}
=> (1-1) (1+1)
=> (0) (2)
=> 0
Additional information--->
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1)(a-b)²=a² + b² -2ab
2)(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
3)(a+b)³=a³+b³+3ab(a+b)
4)(a-b)³=a³-b³-3ab(a-b)
5)a³+b³=(a+b) (a²+b²-ab)
6)a³-b³ =(a-b) (a²+b²+ab)
Answer:
Step-by-step explanation:
a + 1/a = 1
To find ↔↔(1-a+a²) (1+a-a²)=?
, a + 1/a = 1
Multiplying both sides by a => a×a + a×(1/a)=a×1
=> a² + 1 =a
=> a² - a =-1
Now
(1-a+a²)(1+a-a²)
[1+(a²-a)][(1-(a²-a)]
Now putting a²-a=-1 in it
=> {1+(-1)} {1-(-1)}
=> (1-1) (1+1)
=> (0) (2)
=> 0