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1/(1 + a + b⁻¹) + 1/(1 + b + c⁻¹) + 1/(1 + c + a⁻¹) = 1 if abc = 1
Step-by-step explanation:
1/(1 + a + b⁻¹) + 1/(1 + b + c⁻¹) + 1/(1 + c + a⁻¹)
= 1/(1 + a + 1/b) + 1/(1 + b + 1/c) + 1/(1 + c +1/a)
abc = 1
=> ac = 1/b
or b = 1/ac
= 1/(1 + a + ac) + 1/(1 + 1/ac + 1/c) + 1/(1 + c +1/a)
= 1/(1 + a + ac) + ac/(ac + 1 + a) + a/(a + ac + 1)
= 1/(1 + a + ac) + ac/(1 + a + ac) + a/(1 + a + ac)
= (1 + ac + a)/(1 + a + ac)
= (1 + a + ac)/(1 + a + ac)
= 1
1/(1 + a + b⁻¹) + 1/(1 + b + c⁻¹) + 1/(1 + c + a⁻¹) = 1 if abc = 1
Learn more:
If a + b + c = 1, a2+b2+c2=9, a3+b3+c3=1 find 1/a + 1/b + 1/c
https://brainly.in/question/11392304
xyz×abba=xyzxyz find (a+b)=? - Brainly.in
https://brainly.in/question/12220326
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