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If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is?
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If alfa and bita are the roots of x^2= x 1 then value of alfa square/...
Solution:
Given
- Roots of the given equation x^2 = x + 1 are alfa and bita
- We need to find the value of (alfa^2/bita) - (bita^2/alfa)
Calculation
- Let's find the value of alfa + bita first
- By Vieta's formula, alfa + bita = 1
- Now, let's square the above equation
- (alfa + bita)^2 = 1^2
- alfa^2 + 2alfa*bita + bita^2 = 1
- alfa^2 + bita^2 = 1 - 2alfa*bita
- Now, let's find the value of alfa*bita
- Again, by Vieta's formula, alfa*bita = 1
- We can substitute this value in the above equation
- alfa^2 + bita^2 = 1 - 2
- alfa^2 + bita^2 = -1
- We know that (alfa - bita)^2 = alfa^2 + bita^2 - 2alfa*bita
- Substituting the values of alfa^2 + bita^2 and alfa*bita, we get
- (alfa - bita)^2 = -1 - 2
- (alfa - bita)^2 = -3
- alfa - bita = sqrt(-3) or alfa - bita = -sqrt(-3)
- We can simplify this further
- alfa - bita = i*sqrt(3) or alfa - bita = -i*sqrt(3)
- Now, let's find the value of alfa^2/bita - bita^2/alfa
- We can substitute the value of alfa - bita in this expression
- alfa^2/bita - bita^2/alfa = (alfa^3 - bita^3)/(alfa*bita)
- We can simplify this using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2)
- alfa^2/bita - bita^2/alfa = [(alfa - bita)(alfa^2 + alfa*bita + bita^2)]/1
- Substituting the values of alfa - bita and alfa^2 + alfa*bita + bita^2, we get
- alfa^
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If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is?
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If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is?.
If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alfa and bita are the roots of x^2= x 1 then value of alfa square/ bita- bita square/alfa is?.
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