Question

If a=5-2√5, then find a^2​

Answer 1

Answer:

given a = 5 - 2√5.

then, (a)²= (5-2√5)².

[ (a-b)² = a² + b² - 2ab ]

=> (a)²= (5)² + (2√5)²- 2(5)(2√5)

= 25 + 20 - 20√5.

= 45 - 20√5.

Step-by-step explanation:

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Answer 2

The value of $a^{2}$ is 5(9 - 4$\sqrt{5}$).

Step-by-step explanation:

Given equation:

a = 5-2$\sqrt{5}$

To find = $a^{2}$

Solution:

a =5-2$\sqrt{5}$

$a^{2}$=$(5-2\sqrt{5}) ^{2}$

We know from the formula:

$(a-b)^{2} =a^{2} -2ab +b^{2}$

Putting the values as a =5 and

b= 2$\sqrt{5}$

$a^{2}$ = $5^{2}$ - 2×5×2$\sqrt{5}$ +$(2\sqrt{5} )^{2}$

$a^{2}$  = 25 - 20$\sqrt{5}$ + 20

$a^{2}$ = 45-20 $\sqrt{5}$

Result:

$a^{2}$ = 5(9 - 4$\sqrt{5}$)

Thus, the value of $a^{2}$ is 5(9 - 4$\sqrt{5}$).

(#SPJ2)