Let's substitute a = √7 into the expression:
3√7(4-5√7) + (√7 - 6)^2
First, let's simplify the first term:3√7(4-5√7) = 3√7(4) - 3√7(5√7) = 12√7 - 15(√7)^2= 12√7 - 15(7)= 12√7 - 105
Now let's simplify the second term:(√7 - 6)^2 = (√7 - 6)(√7 - 6)= (√7)^2 - 6√7 - 6√7 + 36= 7 - 12√7 + 36= 43 - 12√7
Now, putting it all together:3√7(4-5√7) + (√7 - 6)^2= 12√7 - 105 + 43 - 12√7= -105 + 43= -62
Therefore, when a = √7, the expression 3a(4-5a) + (a-6)^2 simplifies to -62.
Let's substitute a = √7 into the expression:
3√7(4-5√7) + (√7 - 6)^2
First, let's simplify the first term:
3√7(4-5√7) = 3√7(4) - 3√7(5√7) = 12√7 - 15(√7)^2
= 12√7 - 15(7)
= 12√7 - 105
Now let's simplify the second term:
(√7 - 6)^2 = (√7 - 6)(√7 - 6)
= (√7)^2 - 6√7 - 6√7 + 36
= 7 - 12√7 + 36
= 43 - 12√7
Now, putting it all together:
3√7(4-5√7) + (√7 - 6)^2
= 12√7 - 105 + 43 - 12√7
= -105 + 43
= -62
Therefore, when a = √7, the expression 3a(4-5a) + (a-6)^2 simplifies to -62.