It is known that the length of the hypotenuse ab of the triangle ABC is √ 5, and the lengths of the two corners are the two real roots of the quadratic equation of one variable χ & # 178; - (2a + 1) χ + 2A = 0 | Math enthusiast | Mathematical art

It is known that the length of the hypotenuse ab of the triangle ABC is √ 5, and the lengths of the two corners are the two real roots of the quadratic equation of one variable χ & # 178; - (2a + 1) χ + 2A = 0

That is, X1 & # 178; + x2 & # 178; = AB & # 178; = 5
x1+x2=2a+1
x1x2=2a
So X1 & # 178; + x2 & # 178;
=(x1+x2)²-2x1x2
=4a²+4a+1-4a
=4a²+1=5
a²=1
a=±1
Because the side length is greater than 0
Then x1x2 = 2A > 0
So a = 1

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