No.1 : (9^x + 9^-x) = 98, maka nilai (3^x + 3^-x) = ... no.2 : x+y=1 dan x^3 + y^3 = 49, maka x^2 + .... Question from @gwenlauren36

October 2018 2 16 Report

No.1 : (9^x + 9^-x) = 98, maka nilai (3^x + 3^-x) = ...

no.2 : x+y=1 dan x^3 + y^3 = 49, maka x^2 + y^2 = ...

makasii

izharulhaq78 $\displaystyle (3^x+3^{-x})^2=(3^x)^2+2\times3^x\times3^{-x}+(3^{-x})^2\\(3^x+3^{-x})^2=3^{x\times2}+2\times3^{x-x}+3^{-x\times2}\\(3^x+3^{-x})^2=3^{2x}+2\times3^{0}+3^{-2x}\\(3^x+3^{-x})^2=(3^2)^{x}+2\times1+(3^2)^{-x}\\(3^x+3^{-x})^2=9^{x}+2+9^{-x}\\(3^x+3^{-x})^2=9^{x}+9^{-x}+2\\(3^x+3^{-x})^2=98+2\\(3^x+3^{-x})^2=100\\3^x+3^{-x}=\sqrt{100}\\\boxed{\boxed{3^x+3^{-x}=10}}$

$\displaystyle (x+y)^3=x^3+3x^2y+3xy^2+y^3\\(x+y)^3=x^3+y^3+3(x^2y+xy^2)\\(x+y)^3=x^3+y^3+3xy(x+y)\\1=49+3xy(1)\\1-49=3xy\\-48=3xy\\-16=xy\\\\(x+y)^2=x^2+2xy+y^2\\(1)^2=x^2+2(-16)+y^2\\1=x^2-32+y^2\\1+32=x^2+y^2\\\boxed{\boxed{33=x^2+y^2}}$

0 votes Thanks 1

imamjhe 1. 9^x + 9^-x = 98
3^2x + 3^-2x = 98
(3^x + 3^-x)^2 - 2 = 98
(3^x + 3^-x)^2 = 100
3^x + 3^-x = 10

2. x^3 + y^3 = 49
(x+y)^3 - 3xy(x+y) = 49
(1)^3 - 3xy(1) = 49
1 - 3xy = 49
-3xy = 48
xy = -16

maka x^2 + y^2 adalah
(x+y)^2 = 1^2
x^2 + 2xy + y^2 = 1
x^2 + y^2 = 1 - 2xy

subtitusi xy ke persamaan

X^2 + y^2 = 1 -2(-16)
x^2 + y^2 = 33

0 votes Thanks 1

About Us

Life Enjoy

" Life is not a problem to be solved but a reality to be experienced! "

Bantuin yg nomor 11 dan 12 dongg pleasee makasi banyakk

[{(0,09^(3/2)).(x-3)} / (0,3^(4x+1))] = 1 nilai x yg memenuhi persamaan adalah ... (no.2)

[ {(5^(1/2) + 2 )^6} - {(5^(1/2) -2 )^6} ] / 8.(5^(1/2)) = ... help me again please? thankyou very much god will always bless ya. ^^ * yg hari itu salah soal

Bantuin yg nomor 18 dong, beneran gak ngertii, makasii x gbu❤

[ {(5^(1/2) + 2 )^6} - {(5^(1/2) -2 )^6} ] / 80^(1/2) = ... help me again please? thankyou very much god will always bless ya. ^^

[{ 7^x + 2.(7^x) + 3.(7^x) + 4.(7^x) + ... + 49.(7^x) } / 25 ] = 343 nilai x yang memenuhi persamaan adalah ... help please, thnks x

Cara cepat mengerjakan : (48 . 27 . 35 . 175 . 245) ^(1/2) adalah .. thankyouu

Jika a^(3/2) = b^(-3/2) . c^(3/4), maka c dinyatakan dalam a dan b adalah... help please? :) thanks

Jika diketahui x + y = 3, maka nilai dari [{9^(x-2y)} . {2^(2x-y+2)}] / [{3^(x-5y)} . {2^(x-2y+1)}]

Recommend Questions

Life Enjoy

Get in touch

Social