17.
а) F(√37 -6)((√37 +6) -(√3 -√2)² =(√37)² -6² - ((√3)² -2√3*√2 +√2)² ) =
37 -36 -(3 -2√6 +2) =1 -5+2√5 =2√6 -4 > 0 ||√6 >√4 =2||.
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б) (√7 +√2)² -(√11 -2√3)*(√12 +√11) =
7 +2√14 +2 -(√11 -√12)(√11 +√12) = 9 +2√14 - ((√11)²-√(12)² ) =
9 +2√14 -(11-12) = 9 +2√14 +1 =10 +2√14 >0.
* * * 2√3= (2²*3) =√(4*3) =√12. * * *
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в) (-√50 +6√2)/(√40 -5√2) = (-√(25*2) +6√2)/ (√40 -√(5²2) ) =
(-5√2 +6√2)/(√40 -√50) =(√2)/(√40 -√50) <0.<br>-------
18.
а) (1/3)*√27 *(1/9)*√243 =(1/3)*3√3 *(1/9)*9√3 = √3*√3 =3.
* * * 27=9*3 =3²*3 ; 243 =81*3 =9²*3 * * *
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б) 2√32 *√216*3√48 =2√(4²*2)*√(6²*6)*3√(4²*3) =8√2*6√6*12√3 =
8*6*12 *(√2*√3*√6) =8*6*12 *6 =3456.
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в) √1024*2√6561*√1600 = 32*(2*81)*40 =32*80*81 =207360.
удачи !