a) Przekształćmy wyrażenie:
(3+5x)(5x−3)(50x2−18)2=25x2−9(2(25x2−9))2=4(25x2−9)
Dla x=−51
4(25⋅(−51)2−9)=4(25⋅251−9)=4(1−9)=4⋅(−8)=−32
b) Przekształćmy równanie:
7(x+73y)2(−2x−3y)2−25x2=7(71(7x+3y))2(2x+3y)2−(5x)2=7⋅491(7x+3y)2(2x+3y−5x)(2x+3y+5x)=
=71(7x+3y)2(3y−3x)(7x+3y)=7x+3y7(3y−3x)
Dla x=97 , y=47
7⋅97+3⋅477(3⋅47−3⋅97)=637+1277(127−277)=7577⋅(−157)=
=−5⋅1577⋅157=−57=−152=−1104=−1,4
c) Przekształćmy równanie:
x2+x+1x4−x−x2−x+1x4+x+x+1=
=(x2+x+1)(x2−x+1)(x4−x)(x2−x+1)−(x2+x+1)(x2−x+1)(x4+x)(x2+x+1)+x+1=
=(x2+x+1)(x2−x+1)x6−x5+x4−x3+x2−x−(x2+x+1)(x2−x+1)x6+x5+x4+x3+x2+x+x+1=
=(x2+x+1)(x2−x+1)x6−x5+x4−x3+x2−x−x6−x5−x4−x3−x2−x+x+1=
=x4−x3+x2+x3−x2−x+x2−x+1−2x5−2x3−2x+x+1=
=x4+x2+1−2x(x4+x2+1)+x+1=−2x+x+1=−x+1
Dla x=349
−349+1=1−349
d) Przekształćmy równanie:
x+yy−(x+y)2xy−x2−y2xy=
=(x+y)2(x−y)y(x+y)(x−y)−(x+y)2(x−y)xy(x−y)−(x−y)(x+y)(x+y)xy(x+y)=
=(x+y)2(x−y)y(x2−y2)−(x+y)2(x−y)x2y−xy2−(x+y)2(x−y)x2y+xy2=
=(x+y)2(x−y)x2y−y3−x2y+xy2−x2y−xy2=(x+y)2(x−y)−y3−x2y=(x+y)2(x−y)−y(y2+x2)
Dla x=23 , y=32
(23+32)2(23−32)−32((32)2+(23)2)=(4⋅3+2⋅23⋅32+9⋅2)(23−32)−32(9⋅2+4⋅3)=
=(12+126+18)(23−32)−32(18+12)=(30+126)(23−32)−32⋅30=
=603−902+2418−3612−902=603−902+722−723−902=
=−123−182−902=−6(23+32)−6⋅152=23+32152=
=(23)2−(32)2152(33−32)=4⋅3−9⋅2306−45⋅2=12−18306−90=
=−6306−90=−56+15=15−56
