Question

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$wx^{2} x^{2} =$

Answer 1

Answer:

STEP

1

:

w - x

Simplify —————

x

Equation at the end of step

1

:

((w2) - (x2)) (w - x)

————————————— ÷ ———————

wx x

STEP

2

:

w2 - x2

Simplify ———————

wx

Trying to factor as a Difference of Squares:

2.1 Factoring: w2 - x2

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 : w2 is the square of w1

Check : x2 is the square of x1

Factorization is : (w + x) • (w - x)

Equation at the end of step

2

:

(w + x) • (w - x) (w - x)

————————————————— ÷ ———————

wx x

STEP

3

:

(w+x)•(w-x) w-x

Divide ——————————— by ———

wx x

3.1 Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

(w + x) • (w - x) w - x (w + x) • (w - x) x

————————————————— ÷ ————— = ————————————————— • ———————

wx x wx (w - x)

Canceling Out :

3.2 Cancel out (w - x) which appears on both sides of the fraction line.

Canceling Out :

3.3 Canceling out x as it appears on both sides of the fraction line

Final result :

w + x

—————

w

Answer 2

Answer:

Need to find: The three angles of ∆?

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❍ Let's say the smaller angle be x. Then, the largest angle and another angle would be (4x + 5) and 2x.

$\begin{gathered}\underline{\bigstar\:{\pmb{\textsf{Angle Sum Property of}} \: \sf{\Delta} \;:}}\\\end{gathered}$

The ASP (Angle Sum Property) of the triangle States that the Sum of all angles of the triangle is 180°.

⠀

$\begin{gathered}:\implies\sf x + 4x + 5 + 2x = 180^\circ\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 7x + 5 = 180^\circ\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 7x = 180^\circ - 5\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 7x = 175\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf x = \cancel\dfrac{175^\circ}{7}\\\\\\\end{gathered}$

$\begin{gathered}:\implies\underline{\boxed{\pmb{\frak{\purple{x = 25^\circ}}}}}\;\bigstar\\\end{gathered}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Angles\;of\;the\:\Delta\:are\; :}}$

⠀⠀⠀⠀

x = 25°

(4x + 5) = (4[25] + 5) = 105°

2x = 2(25) = 50°

⠀

$\therefore{\underline{\sf{Hence, \: the \: angles \: of \: \Delta \: are \: \pmb{ 25^\circ, \; 105^\circ,\; 50^\circ} \: respectively}}}$

$\huge\mathtt\red{\textsf{MissEleGant}}$