Question

Proszę o pomoc zadanie 13 w załączniku

Answer 1

13)

a) 3/(√3-1) = 3(√3+1)/[(√3-1)(√3+1)] = 3(√3+1)/(3-1)= 3(√3+1)/2 = 1,5(√3+1)

b) 4/(√2+3) = 4(√2-3)/[(√2+3)(√2-3)] = 4(√2-3)/(2-9) = 4(3-√2)/7

c) √3/(√3+1) = √3(√3-1)/[(√3+1)(√3-1)] = (3-√3)/(3-1)=(3-√3)/2 = 0,5(3-√3)

d) 2√6/(√3-2)= 2√6(√3+2)/[(√3+2)(√3-2)]=2(√18+2√6)/(3-4)=

= -2(√(2*9)+2√(2*3)) =-2√2(3+2√3)

e) 1/(√3-√2) = 1*(√3+√2)/[(√3+√2)(√3-√2)] = (√3+√2)/(3-2) = √3+√2

f) 2/(√6+√2) =  2(√6-√2)/[(√6-√2)(√6+√2)] = 2(√6-√2)/(6-2) =(√6-√2)/2 = 0,5(√6-√2)

g) (√3+2)/(√3-2) =-(√3+2)²/[(√3+2)(2-√3)] =-(3+4+2*2*√3)/(4-3) = -7-4√3

h) (√2-1)/(2√2+1) = (√2-1)(2√2-1)/[(2√2-1)(2√2+1)] = (4-√2-2√2+1)/(4*2-1) =

= (5-3√2)/7