- b. 21 ( + ) = 21=
21 ( ) = 10- d.(2 + 3 x)^2 = 4 + (2)( 3 x) + ( 3 x)(2) +
( 3 x)^2 = 4+4 3 x+ 3x - a.
( 3 + 7 )(2 3 – 5 7 ) = ( 3 )( 2 3 ) +
( 7 )(2 3 ) – ( 3 )(5 7 ) – ( 7 )(5 7 ) =
2( 3 )^2 = 2 7 3 – 5 3 7 – 5( 7 )^2 = 2 3
+ 2 21 – 5 21 – 57 = 6 – 3 21 – 35 =
–29 – 3 21 - d. = = =
= = –- d. = =
= =Set 39 (Page 94)
- a.Square both sides of the equation and then
solve for x:
7 + 3x= 4
(7 + 3x)^2 = (4)^2
7 + 3x= 16
3 x= 9
x= 3Substituting this value into the original
equation yields the true statement 4 = 4,
so we know that it is indeed a solution.- a.Square both sides of the equation and then
solve forx:
4 x+ 33= 2x – 1
( 4 x+ 33)^2 = (2x – 1)^2
4 x+ 33 = 4x^2 – 4x+ 1
0 = 4x^2 –8x–32
0 = 4(x^2 –2x–8)
0 = 4(x– 4)(x+ 2)
x= 4, –2Substituting x = 4 into the original equation
yields the true statement 7 = 7, but substitut-
ing x = –2 into the original equation results in
the false statement 5 = –5. So, only x= 4 is a
solution to the original equation.- e.a = (a)^2 = 6^2 = 36.
- d.Observe that (–^13 )–2= (–1)–2(^13 )–2=
1(–1)^2 ^31
2
= 9. We must solve the equation
(p)^4 = 9 for p. Since, (p)^4 = (p)^4 =
p^2 , this equation is equivalent to p^2 = 9,
the solutions of which are –3 and 3.- d.To eliminate the radical term, raise both
sides to the third power and solve for x:
^35 x – 8= 3
5 x– 8 = 3^3 = 27
5 x= 35
x= 7Substituting this value into the original equa-
tion yields the true statement 3 = 3, so it is
indeed a solution.- b.To eliminate the radical term, raise both
sides to the third power and solve for x:
^37 3 x= –2
7–3x= (–2)^3 = –8
–3x= –15
x= 5Substituting this value into the original equa-
tion yields the true statement –2 = –2, so it is
indeed a solution.- a.Take the square root of both sides and solve
for x:
(x–3)^2 = –28
(x–3)^2 = ±–28
x– 3 = ±2i 7
x= 3 ±2i 7 ^12^43 ^23^2 ^2 x+ 6x
4 – 9x
^2 ^2 x+ 3(2x)
4 – 3^2 (x)^2
2(^2 x) + (3x)(^2 x)
22 – (3x)^22 + 3x
2 + 3x
^2 x
2 – 3x
^2 x
2 – 3x3+5^2
41
3 + 5^2
9 – 25(2)
3 + 5^2
9 – 5^2 ( 2 )^23 + 5^2
32 –(5 2 )^2
3 + 5^2
3 + 5 2
^1
3 – 5 2
^1
3 – 5 2 3 + 7
21 ^3 ^3 + ^7 ^7
7 3 ^7
3
^3
7 ANSWERS & EXPLANATIONS–