Question

Calculați: (2√5-3)²+(3√5+2)²-(√5-√3)(√5+√3)

Answer 1

(2√5-3)²= (2√5)²-2•2√5•3+3²= 20-12√5+9
(3√5+2)²= (3√5)²+2•3√5•2+2²= 45+12√5+4
(√5-√3)(√5+√3)= √5²-√3²= 5-3=2
20-12√5+9+45+12√5+4-2=20+9+45+4-2=76

Answer 2

( 2 √5 - 3 ) ² =
=( 2 √5 ) ² - 2 × 2 √5 × 3 + 3 ²=
=20 - 12 √5 + 9

( 3 √5 + 2 ) ² =
= ( 3 √5 ) ² + 2 × 3 √5 × 2 + 2 ² =
= 45 + 12 √5 + 4

(√5-√3)(√5+√3)=
* FORMULĂ: (a-b)(a+b)=a²-b² *
=√5 ² - √3 ² =
= 5 - 3 =
= 2

( 2 √5 - 3 ) ² + ( 3 √5 + 2 ) ² - ( √5 - √3 ) ( √5 + √3 ) =
= 20 -12 √5 + 9 + 45 + 12 √5 + 4 - 2 =
= 20 + 9 + 45 + 4 - 2 =
= 78 - 2 =
= 76