math

Question

if If 1 + √7 = z – 3, what is the value of (z + 3)^2?
A) 8 + 2√7
B) 14(4 +√7)
C) (2 + √7)^2
D) None of these

Abhishek009 · Answer

1 + √7 = z – 3

Or,  z = 4 + √7

Now,  z + 3 = 7 + √7

So,  (z + 3)^2 = 49 + 14√7 + 7

Or,  (z + 3)^2 = 56 + 14√7

Or,  (z + 3)^2 = 14( 4 + √7) , Answer will be (B)

Kinshook · Answer

Asked: If 1 + √7 = z – 3, what is the value of (z + 3)^2?

z + 3 = 7 + √7 = √7(1+√7)
(z + 3)ˆ2 = (√7(1+√7))ˆ2 = 7 (1 + 7 + 2√7) = 7 (8 + 2√7) = 56 + 14√7 = 14(4 + √7)

IMO B

Crytiocanalyst · Answer

1 + √7 = z – 3

=> 4 + √7 = z

=>7+√7 = z+3 
sq on both sides

=>56+ 14√7 = (z + 3)^2

Therefore IMO B

Fdambro294 · Answer

If you take the 2 quadratic templates:

(square of a sum) - (square of a difference) =

(a + b)^2 - (a - b)^2 = +4ab

In this case:

(z - 3) = (a - b)

Which means ———> a = z — and — b = 3

(z + 3)^2 - (z - 3)^2 = 4(z)(3)

Substitute: (z - 3) = 1 + sqrt(7)

And

Substitute: z = 4 + sqrt(7)

(z + 3)^2 - (1 + sqrt(7))^2 = 12(4 + sqrt(7))

Solving for (z + 3)^2 ——->

+   =

56 + 14*sqrt(7) =

14 (4 + sqrt(7))

B

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