Question

РЕШИТЕ ПЖЖ!!! ДАЮ 100 БАЛЛОВ ТОМУ КТО ВСЕ РЕШИТ

Answer 1

$78\cdot 82 =(80-2)\cdot(80+2)=80^2 -2^2=6400-4=6396 \\ \\ 93^2=(100-7)^2=100^2-2\cdot 100 \cdot 7+7^2=10000-1400+49=8600+49=8649 \\ \\ 84^2-74^2=(84-74)\cdot(84+74)=10\cdot 158=1580 \\ \\ 73^2-2\cdot73\cdot 43+43^2=(73-43)^2=30^2=900$

$(5x+3)^2=(5x)^2+2\cdot 5x \cdot 3 +3^2=25x^2+30x+9 \\ \\ (x+1)^3=x^3+3\cdot x^2 \cdot 1 +3\cdot x \cdot 1^2+1^3 = x^3+3x^2+3x+1 \\ \\ (2x+5y)\cdot(2x-5y)=(2x)^2-(5y)^2=4x^2-25y^2 \\ \\ (7-4y)\cdot (49+28y+16y^2)=(7-4y)\cdot (7^2+ 7 \cdot 4y+(4y)^2)=7^3-(4y)^3=343-64y^3 \\ \\ x^3-64y^3=x^3-(4y)^3=(x-4y)\cdot(x^2+4xy+(4y)^2)=(x-4y)\cdot(x^2+4xy+16y^2)$

$\left \{ {{a-b=80} \atop {a^2-b^2=480}} \right. \left \{ {{a-b=80} \atop {(a-b)\cdot(a+b)=480}} \right. \left \{ {{a-b=80} \atop {80\cdot(a+b)=480}} \right. \left \{ {{a-b=80} \atop {a+b=6}} \right. \left \{ {{a-(6-a)=80} \atop {b=6-a}} \right. \left \{ {{a-6+a=80} \atop {b=6-a}} \right. \\ \\ \left \{ {{2a=86} \atop {b=6-a}} \right. \left \{ {{a=43} \atop {b=6-43}} \right.\left \{ {{a=43} \atop {b=-37}} \right.$

$(5x-8)^2+(2x-8)\cdot(2x+8)+6x=25x^2-2\cdot 5x\cdot 8 +64 +4x^2-64+6x=\\ \\ = 29x^2-80x+6x=29x^2-74x=x\cdot (29x-74)$

$(5x-8)^2+(2x-8)\cdot(2x+8)+6x =x\cdot (29x-74) \\ \\ x=-2 \\ \\ (-2)\cdot (29\cdot(-2)-74)=(-2)\cdot(-58-74)=(-2)\cdot (-132)=264$