Question

a = (1+√3+√2), then the value of (2a4-8a³-5a² +26a-28)ans plz​

Answer 1

Step-by-step explanation:

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Answer 2

Correct Question

a = (1+√3+√2), then the value of 2a⁴-8a³-5a² +26a-28

Answer

The answer is 6√6

Given

a = 1 + √3 + √2

To Find

Value of 2a⁴-8a³-5a² +26a-28

Solution

a = 1 + √3 + √2

a² = (1 + √3 + √2)²

We know that (x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz

Therefore applying this we get

= 1² + √3² + √2² +  2(√3 X 1) + 2(√2 X 1) + 2(√3 X √2)

= 1 + 3 + 2 + 2√3 + 2√2 + 2√6

= 6 + 2√3 + 2√2 + 2√6

a³ = a X a²

= (4 + 2√3 + 2√2 + 2√6)( 1 + √3 + √2)

= 6 + 6√3 + 6√2 + 6√3 + 6 + 2√6 + 2√2 + 2√6 + 4 + 2√6 + 2√18 + 2√12

We know that √18 = 3√2 and √12 = 2√3. Using this here we get,

=  6 + 6√3 + 6√2 + 6√3 + 6 + 2√6 + 2√2 + 2√6 + 4 + 2√6 + 26√3 + 4√3

=  16 + 12√3 + 14√2 + 6√6

a⁴ = (a)²

= (6 + 2√3 + 2√2 + 2√6)²

We know that

(p + q + r + s)² = p² + q² + r² + s² + 2pq + pr + 2ps + 2qr + 2rs

Therefore, by applying this we get

6² + (2√3)² + (2√2)² + (2√6)² + 24√3 + 24√2 + 24√6 + 2(2√3 X 2√2) + 2(2√3 X 2√6) + 2(2√2 X 2√6)

= 36 + 12 + 8 + 24 + 24√3 + 24√2 + 24√6 + 8√6 + 8√18 + 8√12

= 80 + 24√3 + 24√2 + 24√6 + 8√6 + 24√2 + 16√3

= 80 + 40√3 + 48√2 + 32√6

2a⁴-8a³-5a² +26a-28

= 2(80 + 40√3 + 48√2 + 32√6) - 8(16 + 12√3 + 14√2 + 6√6)

- 5(6 + 2√3 + 2√2 + 2√6) + 26( 1 + √3 + √2) + 28

= 160 + 80√3 + 96√2 + 64√6

 -128  - 96√3 - 112√2 -  48√6

   -30  -  10√3 -  10√2 -  10√6

 + 26  + 26√3 + 26√2              

 - 28

=     0   +        0 +        0  +  6√6

= 6√6

Therefore, the answer is 6√6

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