Question

find the value of p if 441 - p ^2 = (21) ^2 - (17)^2​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step

1

:

(441 - (p2)) - ((212) - 172) = 0

STEP

2

:

2.1 21 = 3•7

(21)2 = (3•7)2 = 32 • 72

Equation at the end of step

2

:

(441 - (p2)) - ((32•72) - 172) = 0

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: 289-p2

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 : 289 is the square of 17

Check : p2 is the square of p1

Factorization is : (17 + p) • (17 - p)

Equation at the end of step

3

:

(p + 17) • (17 - p) = 0

STEP

4

:

Theory - Roots of a product

Answer 2

Answer:

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