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If 1/(3-"√"5) - (2+"√"5)/(3+"√"5) = a + b"√"c, find the value of a, b and c.
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Answer
Step-by-step solution
6 stepsRationalize the first term .
To rationalize the denominator, multiply the numerator and denominator by the conjugate of , which is .
Rationalize the second term .
To rationalize the denominator, multiply the numerator and denominator by the conjugate of , which is .
Expand the numerator:
The denominator is .
So, the second term becomes:Substitute the simplified terms back into the original equation.
Combine the terms on the left-hand side.
Find a common denominator, which is 4.
Combine the rational parts and the irrational parts:
Separate the rational and irrational parts to match the form .
This can be written as:
Compare the terms to find the values of , , and .
By comparing the rational parts:
By comparing the coefficients of :
By comparing the radicands:
The values are:
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