Dont know if the radicals will show up..
2�ã3(�ã243-2)-�ã2(5+7�ã2) Can be expanded and simplified to the form
p + q�ã2 + r�ã3. the value of p + q + r is_____
First I simplified the V243 and I got 9V3
2V3(9V3-2)-V2(5+7V2)
18V9-4V3-5V2-7V2
54-4V3-5V2-7V2
54-4V3-12V2
But this just doesnt work out, and i have no idea what ive done wrong.
2√3(√243-2)-√2(5+7√2)
= 2√729 - 4√3 - 5√2 - 7√4
= 54 - 4√3 - 5√2 - 14
= 40 - 4√3 - 5√2
comparing this with
p + q√2 + r√3
p=40, q= -5, and r = -4
so p+q+r = 40-5-4 = 31
check my arithmetic.
Ok, so I missed out the 4, and ended up writing 7V2. That missing out the 4 messed up everything, and yup you are right, thanks a bunch =D
To simplify the expression 2�ã3(�ã243-2)-�ã2(5+7�ã2) and obtain the form p + q�ã2 + r�ã3, let's go step by step to identify any mistakes you might have made:
Step 1: Simplify radical expressions inside parentheses
�ã243 can be simplified to 9�ã3, so we get:
2�ã3(9�ã3-2)-�ã2(5+7�ã2)
Step 2: Distribute and combine like terms
Now, let's distribute the terms inside the first parentheses:
2�ã3 * 9�ã3 = 18�ã(3*3) = 18�ã9
2�ã3(-2) = -4�ã3
And distribute the terms inside the second parentheses:
�ã2 * 5 = 5�ã2
�ã2 * 7�ã2 = 7�ã(2*2) = 7�ã4 = 7�ã(2�ã2) = 7�ã(2�ã(2*1)) = 7�ã(2�ã2)
Combining the terms, we have:
18�ã9 - 4�ã3 - 5�ã2 - 7�ã(2�ã2)
Step 3: Simplify the radical expressions
�ã9 can be simplified to 3, so we have:
18 * 3 - 4�ã3 - 5�ã2 - 7�ã(2�ã2)
�ã3 cannot be simplified further, so it remains as -4�ã3.
Similarly, �ã2 cannot be simplified further, so it remains as -5�ã2.
�ã(2�ã2) cannot be simplified further, so it remains as -7�ã(2�ã2).
Combining the simplified terms, we get:
54 - 4�ã3 - 5�ã2 - 7�ã(2�ã2)
Now, we have the expression in the form p + q�ã2 + r�ã3, where p = 54, q = -5, and r = -7.
Finally, we can calculate p + q + r:
p + q + r = 54 + (-5) + (-7) = 42
Therefore, the value of p + q + r is 42.