a and b are real numbers
We have the following expressions:
a² - b² = 9
a.b = 3
Question: what are the value(s) for a and b ?
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a²-b² = 9 => b² = a²-9
a.b = 3 => b = 3/a => b² = 9/a²
a²-9=9/a²
a4-9a²-9 = 0
(a²-4.5)²-20.25-9=0
a²-4.5 = SQRT(29.25)
a = SQRT(SQRT(29.25)+4.5) = 3.1477, b = 3/a = 0.9530
Here we can form on equation that is (a+b) ^2 - (a-b) ^2 = 4ab,
And (a+b) = 9/(a-b) so one quadratic will be formed that is (9/(a-b)) ^2 - (a-b) ^2 = 12 . So after solving this we will get the value of a-b as 2.194 and then value of a+b will be 4.102 after precision.
Then we can find the value of a and b as 3.148 and 0.954.
a=5 b=4
5²=25 4²=16 25-16=9
in a rectangular triangle with hypotenuse = 5 and opposite side = 4 the adjacent side =3