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what can you tell about the numbers 49 and 144...?
yep... so give you have 49x^2 this is the difference of 2 squares... thats why theres a subtraction sign this may help you factorise \[(ax +b)(ax - b)=a^2x^2 - b^2\] after factoring let it equal zero... then solve for x
are there any shortcuts on how to solve it?
well you know 49 and 144 are square number.... so what do you think a and b might be...?
7 and 12
or is it 7x+12 7x-12 ??
thats it so you are solving (7x - 12)(7x + 12) = 0 so really you just need to solve 7x - 12 = 0 and 7x + 12 = 0 hope it makes sense
so the roots are -7 and 12???
no, you need to solve 7x - 12 = 0 then its 7x = 12 x = 12/7 thats one solution. You need to do the other 7x + 12 = 0
the solutions are the roots
7x=-12 x= -12/7
oh okay i understand it now thanks a lot... i have other problem here help me again please.. f(d)=2d^2-10d
i don't know how to solve it because it's not a perfect square number
Do you see a common factor?
Yes, there is another one.
glad to help... lots of good people here to help with the next question
2 and 2d?
u can use a identity here a^2-b^2=(a+b)(a-b)
$$\huge 2d^2-10d= 2d(d - 5)$$
But where's the other squared number?
I don't understand it :(
49x^2-144 can be written as (7x+12)(7x-12) so x =12/7 and -12/7
these are the two roots
That question was answered already @nirmalnema
Do you know how to do it now @MCath?
i don't know this one f(d)=2d^2-10d
can i just divide them into 2d?
This is called the "zero product property." For all real numbers a and b, ab=0 if and only if a=0 or b=0.
Recall that zero times any number is zero.
so the roots are 0 and 5?
but i don't know how did i got 5
$$\Huge2d =0$$ $$\huge or$$ $$\huge d - 5 = 0$$
ooooowwwwww yess I knew it!! I just didn't had the confidence to solve it hehe Thanks a lot :D
You should be extremely confident with the result that 0 times any number is 0.
It is also the reason you can not divide by 0.
then why the -5 is 5 ???
Thank you so much
Thank you for trying to learn something new in mathematics.
thank you for the patience hehe