Question

(1+√5)* (√2+√3)* (√7-2√3)* (2+2√2)* (4-√3+5√2)* (8-3-√5)* (4x-a)(4x+a+2x)(x-a) (x-2)(x+2-x)(x+5) varogg rapid dau coroana 1h​

Answer 1

Răspuns:

Explicație pas cu pas:

(1+√5)² = 1²+2·1·√5+(√5)² = 1+2√5+5 = 6+2√5

Folosim formulele

(a+b)² = a²+2ab+b² ; (a-b)² =  a²-2ab+b²

(√2+√3)² = 2+2√6+3 = 5+2√6

(√7 - 2√3)² = 7-4√21+12 = 19-4√21

(2+2√2)² = 4+8√2+8 = 12+8√2 = 4(3+2√2)

(4√3+5√2)² = 16·3+2·20·√6+25·2 = 48+40√6+50 = 98+40√6

(8-3√5)² = 64-16·3√5+9·5 = 109-48√5

(4x-a)(4x+a+2x)(x-a) = (4x-a)(6x+a)(x-a) =

= (24x²-2ax-a²)(x-a) = 24x³-24ax²-2ax²+2a²x-a²x+a³=

= 24x³-26ax²+a²x+a³

(x-2)(x+2-x)(x+5) = (x-2)·2·(x+5) = (2x-4)(x+5) =

= 2x²+10x-4x-20 = 2x²+6x-20