The Student Room Group

This discussion is now closed.

Check out other Related discussions

uh, binomial thing? easy?

...with these values of a and b, use the result (1 + 2x)^0.5 ≈ (1 + ax)/(1 + bx), with x = -0.01, to obtain an approximation of root 2, in the form p/q.

---

i obtained a and b by expanding and equating the left hand side of the equation above. but now, how does letting x = -0.01 help me get to 2^0.5 ?
(1+2x)^.5

with x as -0.01
=(0.98)^.5

=(2*0.49)^.5

=0.49^.5(2)^.5

=(0.7)*(2)^.5


(2)^.5=(1 - 0.01a)/0.7(1 - 0.01b)

??? is this right im not too sure myself
1-.02 = 49/50

√(49/50) = 7/ √50 = 7/ 5√2 multiplying by √2 = 7√2 /10

is the relation you may be looking for, recognize a similar question.

edit: with the binomial approximation does it ask for a certain degree of accuracy i.e. what power of x are you going up to?
Reply 3
Avatar for Chewwy
Chewwy
OP
17
Infinity_Kev
(1+2x)^.5

with x as -0.01
=(0.98)^.5

=(2*0.49)^.5

=0.49^.5(2)^.5

=(1/7)*(2)^.5


(2)^.5=(1 - 0.01a)/7(1 - 0.01b)

??? is this right im not too sure myself

i presume this line should be 0.7√2? i get the idea, thanks.

Related discussions

Latest

Trending

Trending

Articles for you