Question

If a and b are rational numbers find a and b √5-2/√5+2 - √5+2/√5-2= a+b √5

Answer 1

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Answer 2

a=0 and b=-8.

Step-by-step explanation:

• Irrational numbers are all those numbers in the number line which cannot be expressed as fractions that is these numbers cannot be expressed in the form  $\frac{x}{y}$, where y is not equal to 0.

• According to the given information, the problem is,

√5-2/√5+2 - √5+2/√5-2= a+b√5

Now, we first take lcm on the left hand side since the denominators when taken lcm, correspond to the well-known algebraic identity that is

(a+b).(a-b)=a²-b².

Then, the expression becomes,

$\frac{(\sqrt{5}-2) ^{2}- (\sqrt{5}+2) ^{2}}{1}$

The numerator when simplified becomes $0-8\sqrt{5}$.

Comparing both sides of the equation, we get the values of a and b as a=0 and b=-8.

Hence, the values are a=0 and b=-8.

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