Fractional Expression | MCQs

Explanation

x = 7 — 4√3, we are required to find x + 1/x.

1/x = 1/(7 — 4√3)

Rationalising 1/x,

1/x = {1/(7 —4√3)} × {(7 + 4√3)/7 + 4√3)} = {(7 + 4√3)}/{7² — 4²(√3)²} = (7 + 4√3)/(49 — 48) = 7 + 4√3.

Therefore

x + 1/x = 7 — 4√3 + 7 + 4√3 = 14.

Explanation

Given:

1/4 (3 4/4 + 4 6/8 + 7 3/12)

Simplify each term:

3 4/4 = 3 + 1 = 4

4 6/8 = 4 + 3/4

7 3/12 = 7 + 1/4

Add the terms:

= 1/4 (4 + 4 + 3/4 + 7 + 1/4)

= 1/4 (15 + 3/4 + 1/4)

= 1/4 (15 + 1)

= 1/4 × 16

= 4

Explanation

$$= frac{10 - 1}{10^{10}} = frac{9}{10^{10}} = 9 times 10^{-11}$$