Question

If c^2 + d^2= 4 and (c-d)^2
= 2, what
is the value of cd?​

Answer 1

Answer:

Step-by-step explanation:

Equation (1) c2+d2=4 → (c+d)2=4 → c+d=2 → c=2-d

Equation(2) (c-d)2=2 → c-d=1 → c=1+d

now we get (1)=(2), which by substitution is

2-d = 1+d, let’s solve for d

2–1=d+d → 1=2d = d=1/2

plug d into equation (2)

c=1+d = 1+1/2 = 2/2+1/2 = 3/2

now we know that c=3/2 and d=1/2

before proceeding to calculate for cd, let’s double check our results by plugging them back into the original equations:

(1) (c+d)*2 = (3/2+1/2)*2 = (4/2 )*2 = 2*2 = 4 (correct!)

(2) (c-d)*2 = (3/2–1/2)*2 = 2/2*2 = 1*2 = 2 (correct!)

now we can calculate cd

cd = c*d = 3/2*1/2

cd = 3/4

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