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Find the values of a and $b$ in the given equation and choose the option that follows.

$5 − 6 5 + 6 = a − b 6$

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a = 3119

and

b = 1019

a = 3119

and

b = − 1019

a = − 20

and

b = 30

a = − 10

and

b = 30

answer is A.

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Detailed Solution

We are given an equation as follows,

5 − 6 5 + 6 = a − b 6

.
We have to find the values of a and b such that the given equation holds.
To rationalize the given fraction, we multiply the numerator and the denominator of the expression on the left by

5 − 6

, and simplify using the identity

a + b a − b = a 2 − b 2

5 − 6 5 + 6 = 5 − 6 5 + 6 × 5 − 6 5 − 6 = 5 − 6 2 52 − 62 = 25 − 106 + 6 25 − 6 = 31 − 106 19

Now, equate the resulting expression to the right side of the given equation, i.e.,

a − b 6

, to get the values of a and b as follows,

a − b 6 = 31 − 106 19 a − b 6 = 3119 − 10196

From the above equation, we get the value of a as

3119

and b as

1019

.
Hence, the correct option is (1).

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