$\mathrm{ExOO}^{3}$
\[
\left\{\begin{array}{l}
a^{2}-b^{2}=400 \\
a-b=10
\end{array}\right.
\]
(2) Determinier les reels $a$ et $b$ ?

Answer

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Answer

$\boxed{a = 25, b = 15}$

Steps

Step 1 ：Solve the second equation for a: $a = b + 10$

Step 2 ：Substitute the expression for a into the first equation: $(b + 10)^2 - b^2 = 400$

Step 3 ：Solve the equation for b: $b = 15$

Step 4 ：Find the value of a: $a = 15 + 10 = 25$

Step 5 ：$\boxed{a = 25, b = 15}$