Question

Mik cần bài 4 thôi nha

Answer 1

1: \(BC=\sqrt{5^2+12^2}=13\left(cm\right)\)

\(BH=\dfrac{5^2}{13}=\dfrac{25}{13}\left(cm\right)\)

CH=13-25/13=144/13(cm)

Xét ΔABC vuông tại A có sin C=AB/BC=5/13

nên góc C=22 đọ

=>góc B=68 độ

2:

a: \(DE=AH=\dfrac{AB\cdot AC}{BC}=\dfrac{60}{13}\left(cm\right)\)

b: HB*HC=AH^2

AE*AC=AH^2

DO đó: HB*HC=AE*AC

Answer 2

a) M= \(\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\)
=\(\left(\dfrac{\left(\sqrt{a}+1\right)^2}{a-1}-\dfrac{\left(\sqrt{a}-1\right)^2}{a-1}+\dfrac{4\sqrt{a}\left(a-1\right)}{a-1}\right)\left(\dfrac{a}{\sqrt{a}}-\dfrac{1}{\sqrt{a}}\right)\)
=\(\left(\dfrac{a+2\sqrt{a}+1-a+2\sqrt{a}-1+4a-4\sqrt{a}}{a-1}\right)\left(\dfrac{a-1}{\sqrt{a}}\right)\)
=\(\dfrac{4a}{a-1}.\dfrac{a-1}{\sqrt{a}}\)
=\(4\sqrt{a}\)
Chúc bạn học tốt<3