Question

write any five rational numbers beetween -2 and 0​

Answer 1

Answer:

It is the same as solving

a^2b+b^2a=49/48 with the constraints a,b≥0

and a+b=7/2,

hence it boils down to finding the solutions of

g(a)=a^7−a+(7/2−a)^2a=49/48

over the interval [0,7/2].

g(a)≥2 if a≥1/3

and over [0,1/3] the function g(a) is increasing,

hence there is a unique solution in a right neighbourhood of the origin. By applying few steps of Newton's method with starting point 1/100 we get a≈0.00824505

hence x≈0.00006798.

Answer 2

$\huge\sf{\underline{\underline{\red{Solution}}}}$

$\sf{Rational \: numbers \: between \: -2 \: and \: 0 \: are:-}$

$\sf{-1, -1.5, -1.75, -1.875, -0.9375}$