(根2+根3+根7)分之(根2+根3-根7)

来源：百度知道 编辑：UC知道 时间：2024/05/18 01:17:25
这是一道计算题，请写出过程与答案
可选用方法：平方差公式等
该式的参考答案为
5分之12+7倍根6-4倍根14-3倍根21

(√2 + √3 - √7)/ (√2 + √3 + √7)
=[(√2 + √3 - √7)(√2 + √3 - √7)]/[(√2 + √3 - √7)(√2 + √3 + √7)]
=[(√2 + √3)²+(√7)²-2(√2 + √3)(√7)]/[(√2 + √3)²-(√7)²]
=[2+3+2√6+7-2√14-2√21]/[2+3+2√6-7]
=[12+2√6-2√14-2√21]/[2√6-2]
=[6+√6-√14-√21]/[√6-1]
=[(√6+1)(6+√6-√14-√21)]/[(√6-1)(√6+1)]
=[6√6+6-2√21-3√7+6+√6-√14-√21]/[6-1]
=[12+7√6-4√14-3√21]/5

(√2 + √3 - √7)/ (√2 + √3 + √7)
=[(√2 + √3 - √7)(√2 + √3 - √7)]/[(√2 + √3 - √7)(√2 + √3 + √7)]
=[(√2 + √3)²+(√7)²+2(√2 + √3)(√7)]/[(√2 + √3)²-(√7)²]
=[2+3+2√6+7+2√14+2√21]/[2+3+2√6-7]
=[12+2√6+2√14+2√21]/[2√6-2]
=[6+√6+√14+√21]/[√6-1]
=[(√6+1)(6+√6+√14+√21)]/[(√6-1)(√6+1)]
=[6√6+6+2√21+3√7+6+√6+√14+√21]/[6-1]
=[12+7√6+√14+3√7+3√21]/5