Question-219233

Question Number 219233 by Spillover last updated on 20/Apr/25

Answered by mr W last updated on 20/Apr/25

Commented by mr W last updated on 20/Apr/25

a=25, b=17 a^2 +(r_1 −r_2 )^2 =b^2 +(r_1 +r_2 )^2 ⇒4r_1 r_2 =a^2 −b^2 ⇒r_1 r_2 =((a^2 −b^2 )/4)=((25^2 −17^2 )/4)=84

$${a}=\mathrm{25},\:{b}=\mathrm{17} \\ $$$${a}^{\mathrm{2}} +\left({r}_{\mathrm{1}} −{r}_{\mathrm{2}} \right)^{\mathrm{2}} ={b}^{\mathrm{2}} +\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right)^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{4}{r}_{\mathrm{1}} {r}_{\mathrm{2}} ={a}^{\mathrm{2}} −{b}^{\mathrm{2}} \\ $$$$\Rightarrow{r}_{\mathrm{1}} {r}_{\mathrm{2}} =\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{4}}=\frac{\mathrm{25}^{\mathrm{2}} −\mathrm{17}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{84} \\ $$

Commented by Spillover last updated on 21/Apr/25