Question

va rog ajutatima azi ​

Answer 1

a) A=ab+ba-aa-bb

= 10a+b+10b+a-10a-a-10b-b = 11a+11b-11a-11b= 0 = 0²

b) B=ab+5ba-126

= 10a+b+500+10b+a-126

= 11a+11b+374

= 11(a+b) + 374

a, b - nenule => a+b≥2

Dar a,b - cifre => a+b≤18

=> 2≤a+b≤18 |•11

<=> 22≤11(a+b)≤198 |+374

<=> 396≤11(a+b)+374≤572

Patratele perfecte între 396 si 572={400,441,484,529}

11(a+b)+374=400 => a+b=24/11=2,(18) dar a,b ∈ N => B≠400

11(a+b)+374=441 => a+b=67/11=6,(09) dar a,b ∈ N => B≠441

11(a+b)+374=484 => a+b=110/11=10 => B=484

11(a+b)+374=529 => a+b=155/11=14,(09) dar a,b ∈ N => B≠529

B=484, a+b=10, 1≤a,b≤9

=> I. a=1, b=9

II. a=2, b=8

III. a=3, b=7

IV. a=4, b=6

V. a=5, b=5

VI. a=6, b=4

VII. a=7, b=3

VIII. a=8, b=2

IX. a=1, b=9

I,II,III,IV,V,VI,VII,VIII,IX => ab={19,28,37,46,55,64,73,82,91}