Question

X的平方减去y的平方等于5,X乘以y等于根号14,求X减y的值

Answer 1

X²-y²=5，①
Ⅹy=√14②
求：Ⅹ-y=？
解：√14=√2×√7
√7²-√2²=5
Ⅹ-y=√7-√2

Answer 2

令a=x+y，b=x-y

①x^2-y^2=(x+y)(x-y)=ab=5
②4xy=(x+y)^2-(x-y)^2=a^2-b^2=4√14
由①得：a=5/b，代入②
(5/b)^2-b^2=4√14
b^4+4√14b^2-25=0
(b^2+2√14)^2=81
b^2+2√14=9
b^2=9-2√14
b=±(√7-√2)
所以x-y=√7-√2，或者√2-√7