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If a2 + 8 = 4a then find the value of a4 – a3 + 2a2 + 10
1.  34
2. 20
3. – 38
4. – 40

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Correct Answer - Option 3 : – 38

Given:

a2 + 8 = 4a

Formula used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

a2 + 8 = 4a

Squaring on both side

⇒ (a2 + 8)2 = (4a)2

⇒ a4 + 16a2 + 64 = 16a2

⇒ a4 = – 64      ----1

a2 + 8 = 4a

⇒ a2 = 4a – 8

⇒ a2 = 4(a – 2)

⇒ (a – 2) = a2/4      ----2

To find a4 – a3 + 2a2 + 10

⇒ – 64 – a2(a – 2) + 10

⇒ – 54 – a× a2/ 4  (from equation 2)

⇒ – 54 – a4/4 

⇒ – 54 – (– 64)/4  (from equation 1)

⇒ – 38

∴ The value of a4 – a3 + 2a2 + 10 is – 38

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