Đáp án:

Giải thích các bước giải:

a) x^5y - xy^5 biết x - y =2 ; x^2 + y^2 =4

x^5y - xy^5 <=> xy(x^4-y^4) <=> xy[ (x^2)-(y^2)] <=> xy(x-y)(x+y)(x^2+y^2) <=> 8xy(x+y)

xin lỗi bạn mk chỉ bt làm phần a

$\begin{array}{l} a){x^5}y - x{y^5} = xy\left( {{x^4} - {y^4}} \right)\\ \left\{ \begin{array}{l} x - y = 2\\ {x^2} + {y^2} = 4 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} {\left( {x - y} \right)^2} = 4\\ {x^2} + {y^2} = 4 \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} {x^2} + {y^2} - 2xy = 4\\ {x^2} + {y^2} = 4 \end{array} \right. \Rightarrow xy = 0\\ \Rightarrow {x^5}y - x{y^5} = xy\left( {{x^4} - {y^4}} \right) = 0\\ b){x^5} - 32{y^5}\\ = {x^5} - {\left( {2y} \right)^5}\\ = \left( {x - 2y} \right)\left( {{x^4} + {x^3}.2y + {x^2}.{{\left( {2y} \right)}^2} + x.{{\left( {2y} \right)}^3} + {{\left( {2y} \right)}^4}} \right)\\ + ){x^4} + {x^3}.2y + {x^2}.{\left( {2y} \right)^2} + x.{\left( {2y} \right)^3} + {\left( {2y} \right)^4}\\ = \left( {{x^4} + 2{x^2}.{{\left( {2y} \right)}^2} + {{\left( {2y} \right)}^4}} \right) - {x^2}.{\left( {2y} \right)^2} + {x^3}.2y + x.{\left( {2y} \right)^3}\\ = {\left( {{x^2} + {{\left( {2y} \right)}^2}} \right)^2} + 2xy\left( {{x^2} - 2xy + 4{y^2}} \right)\\ = {\left( {{{\left( {x + 2y} \right)}^2} - 2.x.2y} \right)^2} + 2xy\left( {{{\left( {x + 2y} \right)}^2} - 6xy} \right)\\ = {\left( {{7^2} - 4.3} \right)^2} + 2.3.\left( {{7^2} - 6.3} \right)\\ = 1555\\ + )x + 2y = 7\\ \Rightarrow {\left( {x + 2y} \right)^2} = 49\\ \Leftrightarrow {x^2} + 4xy + 4{y^2} = 49\\ \Leftrightarrow {x^2} - 4xy + 4{y^2} + 8xy = 49\\ \Leftrightarrow {\left( {x - 2y} \right)^2} + 8xy = 49\\ \Leftrightarrow {\left( {x - 2y} \right)^2} = 49 - 8.3 = 25\\ \Leftrightarrow x - 2y = 5\left( {x > 2y \Rightarrow x - 2y > 0} \right)\\ \Rightarrow {x^5} - 32{y^5} = 5.1555 = 7775 \end{array}$