Question Number 223242 by mnjuly1970 last updated on 19/Jul/25
Answered by Tawa11 last updated on 19/Jul/25
$$\mathrm{Sir},\:\mathrm{did}\:\mathrm{you}\:\mathrm{hear}\:\mathrm{from}\:\:\:\:\:\mathrm{Mathdave}??? \\ $$$$\mathrm{Or}\:\mathrm{you}\:\mathrm{know}\:\mathrm{where}\:\mathrm{he}\:\mathrm{is}? \\ $$
Commented by mnjuly1970 last updated on 19/Jul/25
$$\:\:{hello}\:{sir}\:.\:{no}\:,\:{i}\:{didn}'{t}\:{hear}\:{it}\:. \\ $$
Answered by mr W last updated on 19/Jul/25
Commented by mr W last updated on 19/Jul/25
$$\frac{{x}}{{LM}}=\frac{{b}}{{LN}}\:\:\:…\left({i}\right) \\ $$$$\frac{{x}}{{LN}}=\frac{{a}}{{LM}}\:\:\:…\left({ii}\right) \\ $$$$\left({i}\right)×\left({ii}\right): \\ $$$${x}^{\mathrm{2}} ={ab} \\ $$
Commented by mnjuly1970 last updated on 19/Jul/25
$$\:\cancel{\underline{\underbrace{\lesseqgtr}}} \\ $$
Answered by mr W last updated on 19/Jul/25
Commented by mr W last updated on 19/Jul/25
$$\frac{{x}}{{LM}}=\frac{{b}}{{LN}}\:\:\:\:…\left({i}\right) \\ $$$$\frac{{x}}{{LN}}=\frac{{a}}{{LM}}\:\:\:\:…\left({ii}\right) \\ $$$$\left({i}\right)×\left({ii}\right): \\ $$$${x}^{\mathrm{2}} ={ab} \\ $$
Commented by mnjuly1970 last updated on 19/Jul/25
$$\:\:{grateful}\:\:{sir}\:\:{W} \\ $$
Answered by mr W last updated on 19/Jul/25
Commented by mr W last updated on 19/Jul/25
$$\frac{{a}}{{p}}=\frac{{h}}{{r}}=\frac{{b}}{{q}}\:\Rightarrow\frac{{p}}{{q}}=\frac{{a}}{{b}} \\ $$$$\frac{{x}−{a}}{{p}}=\frac{{b}−{x}}{{q}} \\ $$$$\frac{{x}−{a}}{{b}−{x}}=\frac{{p}}{{q}}=\frac{{a}}{{b}} \\ $$$$\Rightarrow\mathrm{2}{ab}={x}\left({a}+{b}\right) \\ $$$$\Rightarrow\frac{\mathrm{2}}{{x}}=\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\:\checkmark \\ $$