Question

已知X平方加根号2Y=根号3，Y平方加根号2X=根号3，X不等于Y，求XY的值

急 在线等

Answer 1

由已知可知 X*X+√2 * Y=√3，Y*Y+√2 * X=√3两式相减，则有 X*X+√2 * Y =Y*Y+√2 * X ==> (X*X-Y*Y)= √2 * (X-Y) ==> (X-Y)*(X+Y)=√2 * (X-Y) [因为X≠Y] ==> X+Y = √2两式相加，则有 X*X+√2 * Y + Y*Y+√2 * X = 2√3 ==> (X*X + Y*Y)+(√2 * X+√2 * Y) = 2√3 ==> [(X + Y)^2 - 2XY] + √2 * (X+Y) = 2√3 ==> (√2)^2 -2XY + √2 * √2 = 2√3 ==> 4 - 2XY = 2√3 ==> XY = 2 - √3所以 XY = 2 - √3 。