本週的问题

更新于Aug 16, 2021 1:38 PM

本週我们又遇到了equation问题:

你会如何解决p25(2+4p)=970\frac{{p}^{2}}{5(2+4p)}=\frac{9}{70}

开始吧!



p25(2+4p)=970\frac{{p}^{2}}{5(2+4p)}=\frac{9}{70}

1
抽出相同的项22
p25×2(1+2p)=970\frac{{p}^{2}}{5\times 2(1+2p)}=\frac{9}{70}

2
简化 5×2(1+2p)5\times 2(1+2p)10(1+2p)10(1+2p)
p210(1+2p)=970\frac{{p}^{2}}{10(1+2p)}=\frac{9}{70}

3
将两边乘以10(1+2p)10(1+2p)
p2=970×10(1+2p){p}^{2}=\frac{9}{70}\times 10(1+2p)

4
使用此法则:ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
p2=9×10(1+2p)70{p}^{2}=\frac{9\times 10(1+2p)}{70}

5
简化 9×10(1+2p)9\times 10(1+2p)90(1+2p)90(1+2p)
p2=90(1+2p)70{p}^{2}=\frac{90(1+2p)}{70}

6
简化 90(1+2p)70\frac{90(1+2p)}{70}9(1+2p)7\frac{9(1+2p)}{7}
p2=9(1+2p)7{p}^{2}=\frac{9(1+2p)}{7}

7
将两边乘以77
7p2=9(1+2p)7{p}^{2}=9(1+2p)

8
扩展。
7p2=9+18p7{p}^{2}=9+18p

9
将所有项移到一边。
7p2918p=07{p}^{2}-9-18p=0

10
7p2918p7{p}^{2}-9-18p中的第二项分为两个项。
7p2+3p21p9=07{p}^{2}+3p-21p-9=0

11
抽出前两个项中的因数,然后抽出后两个项的因数。
p(7p+3)3(7p+3)=0p(7p+3)-3(7p+3)=0

12
抽出相同的项7p+37p+3
(7p+3)(p3)=0(7p+3)(p-3)=0

13
求解pp
p=37,3p=-\frac{3}{7},3

完成

小数形式:-0.428571, 3