find the area of triangle of vertices (a,a),(a+1,a+1),(a+2,a)
Answers
Answer:
Step-by-step explanation:
Step 1 :
1
Simplify —
a
Equation at the end of step 1 :
1 1
(a + —) ÷ (— - a)
a a
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using a as the denominator :
a a • a
a = — = —————
1 a
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 - (a • a) 1 - a2
——————————— = ——————
a a
Equation at the end of step 2 :
1 (1 - a2)
(a + —) ÷ ————————
a a
Step 3 :
1
Simplify —
a
Equation at the end of step 3 :
1 (1 - a2)
(a + —) ÷ ————————
a a
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using a as the denominator :
a a • a
a = — = —————
1 a
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
a • a + 1 a2 + 1
————————— = ——————
a a
Equation at the end of step 4 :
(a2 + 1) (1 - a2)
———————— ÷ ————————
a a
Step 5 :
a2+1 1-a2
Divide ———— by ————
a a
5.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
a2 + 1 1 - a2 a2 + 1 a
—————— ÷ —————— = —————— • ————————
a a a (1 - a2)
Polynomial Roots Calculator :
5.2 Find roots (zeroes) of : F(a) = a2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 2.00
1 1 1.00 2.00
Polynomial Roots Calculator found no rational roots
Trying to factor as a Difference of Squares :
5.3 Factoring: 1 - a2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : a2 is the square of a1
Factorization is : (1 + a) • (1 - a)
Final result :
a2 + 1
—————————————————
(a + 1) • (1 - a)
Processing ends successfully
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