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If 2a – 2−a = , what is the value of 4a + 4−a ?

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Joined: 07 Dec 2018
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If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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08 Dec 2018, 07:37
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55% (hard)

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53% (01:32) correct 47% (02:00) wrong based on 53 sessions

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If $$2^a – 2^{−a}$$= $$\sqrt{7}$$ , what is the value of$$4^a + 4^{−a}$$ ?

A. 1
B. 7
C. 9
D. 49
E. It cannot be determined from the information given.
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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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08 Dec 2018, 07:56
1
Squaring $$2^a - 2^{-a}$$ gives, $$(2^a - 2^{-a})^2$$ = $$4^a+4^{-a}-2*2^a*2^{-a}$$

$$(\sqrt{7})^2$$ = $$4^a+4^{-a}-2*2^a*2^{-a}$$

7 = $$4^a+4^{-a}-2*1$$

9 = $$4^a+4^{-a}$$

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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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08 Dec 2018, 08:04
1
OA:C

$$2^a – 2^{−a}$$= $$\sqrt{7}$$

Squaring both sides, we get
$$2^{2a}+2^{−2a}-2*2^a*2^{-a}=7$$
$$4^a+4^{-a}-2=7$$
$$4^a+4^{-a}=9$$
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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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08 Dec 2018, 08:06
2
Scmfanatic wrote:
If $$2^a – 2^{−a}$$= $$\sqrt{7}$$ , what is the value of$$4^a + 4^{−a}$$ ?

A. 1
B. 7
C. 9
D. 49
E. It cannot be determined from the information given.

$$4^a + 4^{−a}$$ = $$2^2a + 2^{−2a}$$

given,
$$2^a – 2^{−a}$$= $$\sqrt{7}$$ ; squaring both sides
(a-b)^2 = a^2+b^2-2ab ; we get $$2^2a + 2^{−2a} - 2$$ = 7
solving we get $$2^2a + 2^{−2a}$$ = 9 C
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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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08 Dec 2018, 08:08
1
Important thing to note in this question is whenever you have a number and its reciprocal then remember that when ever you mutiply them would give you one. Also looking at the numbers you should note that (A + B)^2 = A^2 + B^2 + 2AB should do the trick in this question.

Option C is the correct answer.
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If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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05 Feb 2019, 20:27
Afc0892 wrote:
Squaring $$2^a - 2^{-a}$$ gives, $$(2^a - 2^{-a})^2$$ = $$4^a+4^{-a}-2*2^a*2^{-a}$$

$$(\sqrt{7})^2$$ = $$4^a+4^{-a}-2*2^a*2^{-a}$$

7 = $$4^a+4^{-a}-2*1$$

9 = $$4^a+4^{-a}$$

Good night Afc0892 !

Would you be so kind and explain to me how do you go from 2^a*2^{-a} to *1?

Kind regards!
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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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05 Feb 2019, 21:01
1
jfranciscocuencag wrote:
Afc0892 wrote:
Squaring $$2^a - 2^{-a}$$ gives, $$(2^a - 2^{-a})^2$$ = $$4^a+4^{-a}-2*2^a*2^{-a}$$

$$(\sqrt{7})^2$$ = $$4^a+4^{-a}-2*2^a*2^{-a}$$

7 = $$4^a+4^{-a}-2*1$$

9 = $$4^a+4^{-a}$$

Good night Afc0892 !

Would you be so kind and explain to me how do you go from 2^a*2^{-a} to *1?

Kind regards!

Hey jfranciscocuencag, sure

$$2^a*2^{-a}$$ can be written as $$2^a*\frac{1}{2^a}$$ then $$2^a$$ will be cancelled out.

Hope it helps
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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?  [#permalink]

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07 Feb 2019, 19:44
Scmfanatic wrote:
If $$2^a – 2^{−a}$$= $$\sqrt{7}$$ , what is the value of$$4^a + 4^{−a}$$ ?

A. 1
B. 7
C. 9
D. 49
E. It cannot be determined from the information given.

We can square both sides of the given equation and obtain:

(2^a - 2^(-a))^2 = (√7)^2

4^a + 4^(-a) - 2 = 7

4^a + 4^(-a) = 9

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Re: If 2a – 2−a = , what is the value of 4a + 4−a ?   [#permalink] 07 Feb 2019, 19:44
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