please help me tomorrow is my math exam and i am so weak at math please please help me friends ans all the questions please
Answers
this is the answer of question 2
2.Given √2 is irrational number.
Let √2 = a / b wher a,b are integers b ≠ 0
we also suppose that a / b is written in the simplest form
Now √2 = a / b ⇒ 2 = a2 / b2 ⇒ 2b2 = a2
∴ 2b2 is divisible by 2
⇒ a2 is divisible by 2
⇒ a is divisible by 2
∴ let a = 2c
a2 = 4c2 ⇒ 2b2 = 4c2 ⇒ b2 = 2c2
∴ 2c2 is divisible by 2
∴ b2 is divisible by 2
∴ b is divisible by 2
∴a are b are divisible by 2 .
this contradicts our supposition that a/b is written in the simplest form
Hence our supposition is wrong
∴ √2 is irrational number.
5.
By Rationalization,
L.H.S,
×
____________________________
On Nominator,
by formula,
On Denominator,
by formula,
_____________________________________
_____________________________________
Then,
Now,
a =4
b√15 =√15
_______________________
a= 4
b =1
4.Remainder when (x + 3) divides p(x) is
= p(-3) = 3 (-3)3 - 4(-3)2 + 7 (-3) - 5
= 3 (-27) - 4 9 - 21 - 5
= -143
6.ab+ba=1⟹a2+b2−abab=0
Now back to the right hand side
a3+b3=(a+b)(a2−ab+b2)
We can notice that we have
a2+b2−abab=0⟹a2+b2−ab=0
Trivially a,b≠0 .
Thus we have
a3+b3=(a+b)(a2−ab+b2)=(a+b)⋅0=0
The result is
a3+b3=0
7.It is given that a+b = 10 and ab = 21.
Since (a+b)2 = a2 +2ab +b2,
While substituting we get
102 = a2 + 2(21)+b2.
i.e. 100 = a2 + b2 + 42,
a2+ b2= 100 -42 = 58.
Now,
a2 + b2 = (a − b)2 + 2ab
(a − b)2 = [a2 + b2] - 2ab
(a − b)2 = 58 - 2X21
= 58 - 42
= 16
10.(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
(15)^2=83+2(ab+bc+ca)
225–83=2(ab+bc+ca)
142/2=71=ab+bc+ca
a^3+b^3+c^3–3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
=(15)(83–71)
=15×12
=180 , Answer
11.