Cuatro amigos, Andrés, Diego, Jairo y Luis juegan billar y acuerdan que aquel que pierda deberá duplicar la cantidad de dinero d
1 answer:
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<em>ANSWER:</em>
value of "a" is: a= -b√3+7+4√3
value of "b" is:
<em></em>
<em>STEP-BY-STEP EXPLANATION:</em>
<h2><u>how to get the value of "a":</u></h2><h2><u /></h2>
1. <u>(</u>rationalize the denominator)
<u>(2 + √3) </u><u>× (2 + √3)</u> =a + b√3
2. (write the repeated multiplication in exponential form)
<u>(2 + √3)²</u> =a + b√3
3. (use (a + b)² = a² + 2ab + b² to expand the expression)
<u>4 </u>+ 4√3 + <u>3</u> = a + b√3
4. ( add the numbers)
7 + 4√3 = <u>a</u> + b√3
5. (move the <u>variable</u> to the left-hand side and change its sign. then, move the <u>constants</u> to the right-hand side and change their signs)
<h3><u>-a</u> + 7 + 4√3 = b√3 ⇔ -a = b√3 <u>-7 - 4√3</u></h3><u></u>
6. (change the signs on both sides of the equation)
a = -b√3 + 7 + 4√3
<h2><u>how to get the value of "b":</u></h2><h2><u /></h2>1. (rationalize the denominator. then, use the commutative property to reorder the terms)
(2 + ) × (2 +
) = <u>a + b</u>
→ <u>(2 + </u>
<u>) × (2 +</u>
<u> )</u> = a +
b
2. (write the repeated multiplication in exponential form)
<u>(2 + √3)²</u> =a + b
3. (use (a + b)² = a² + 2ab + b² to expand the expression)
<u>4</u> + 4 + <u>3</u> = a +
b
4. (add the numbers)
7 + 4 = a +
b
5. (move the expression to the left-hand side and change its sign. then, move the <u>constants</u> to the right-hand side and change their signs)
- b + 7 + 4
= a → -
b = a - 7 - 4
6. (divide both sides of the equation by )
b =
7. (rationalize the denominator)
b =
8. (write all numerators above the common denominator)
b =
there you go! I hope this helped. goodluck! :)