If x=3+root8 and y =3- root 8 find 1/x^2+1/y^2

34

Step-by-step explanation:

x=3+√8

y =3-√8

now,

1/x^2+1/y^2

=1/(3+√8)² + 1/(3-√8)²

= [(3-√8)²+(3+√8)²] / (3+√8)²(3-√8)²            [L.C.M  = (3+√8)²(3-√8)² ]

=[(3-√8+3+√8)²-2(3-√8)(3+√8) ] / [(3+√8)(3-√8)]²  

=[6²-2.(3²-√8² )] / (3²-√8²)²                 [ a²+ b²=(a+b)²-2ab]

=[36-2(9-8) ]/ (9-8)²

=[36-2.1] / 1²

=34

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

b