Question

d) VVD
duceti la forma cea mai simplă expresia:
a) 3120-3145+415;
(15-2)(5+2);
b) (2-13);
d) (6-72)2 – (5+2).
ti la forma cea mai simplă expresia:​

Answer 1

Răspuns:

Explicație pas cu pas:

a)3√20-3√45+4√5=3*2√5-3*3√5+4√5=6√5-9√5+4√5=√5

b)(3-√3)²=3²-2*3*√3+(√3)²=9-6√3+3=12-6√3=6(2-√3)

( 2 - √3)² = 2² - 2 × 2 × √3 + 3 = 4 - 4√3 + 3 = 7 - 4√3

c)(√5-2)(√5+2)=(√5)²-2²=5-4=1

d)(6-√2)²-(5+√2)²=6²-2*6*√2+(√2)²-5²-2*5*√2-(√2)²=36-12√2+2-25-10√2-2=11-22√2=11 ( 1 - 2√2)

Answer 2

Răspuns:

Explicație pas cu pas:

a)  

3√20 - 3√45 + 4√5 = √5

√20 = √(4×5) = 2√5

√45 = √(9×5) = 3√5

= 3 × 2√5 - 3 × 3√5 + 4√5 =

= 6√5 - 9√5 + 4√5 =

= - 3√5 + 4√5 =

= √5

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b)

( 2 - √3)² = 2² - 2 × 2 × √3 + 3 = 4 - 4√3 + 3 = 7 - 4√3

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c)

( √5 - 2)(√5 + 2) = (√5)² - 2² = 5 - 4 = 1

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d)

( 6 - √2)² - ( 5 + √2)² =

= 6² - 2 × 6 × √2 + 2 - ( 5² + 2 × 5×√2 + 2 ) =

= 36 - 12√2 + 2 - ( 25 + 10√2 + 2 ) =

= 38 - 12√2 - 27 - 10√2 =

= 11 - 22√2 =

= 11 ( 1 - 2√2)