Answer:
a = 5 and b =6
Step-by-step explanation:
rationalize the denominator by multiplying the numerator and the denominator of the fraction by the inverse of the denominator: 2 - sqrt5.
((40 + 17 sqrt5) * (2-sqrt5)) / ((2+sqrt5) * (2-sqrt5)) = -5 - (6*sqrt5) / -1
multiply the numerator and the denominator by -1: 5 + 6sqrt5
a = 5 and b = 6
The required value of A = 5 and B = 6
[tex]\frac{40+17\sqrt{5} }{2+\sqrt{5} }= a+b\sqrt{5}[/tex]
A = ? B=?
Fraction is defined as the number of composition constitute the Whole.
[tex]\frac{40+17\sqrt{5} }{2+\sqrt{5} }= a+b\sqrt{5}[/tex]
multiply numerator and denominator by 2-√5
(40+17√5)(2-√5) / (2+√5)(2-√5) = a+b√5
80-40√5+34√5-85/4-5 = a+b√5
5+6 = a+b√5
Thus, the required value of A = 5, B = 6
Learn more about fractions here:
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