Sec 3 Maths Challenging Question

kkhing SG

Hi,

Can someone help to solve this sec 3 challenging question? I tried to solve but couldn't get the answer. Thanks. The answer is x~34.3.

Sec 3 Challenging Question

eagle SG

Why is it challenging?

Square both sides
(x+1) sqrt( (x+1) sqrt (x+1) ) = 2^9
Square both sides again
(x+1)^2 (x+1) sqrt (x+1) = 2^18
or
(x+1)^3 sqrt (x+1) = 2^18
Square both sides again
(x+1)^7 = 2^36
so x+1= 2^ (36/7)
x = 34.3 (use calculator)

wee_ws SG

Hi,

It is understandably challenging for two reasons:

1. The form is atypical to the student.

2. The method of squaring several times is not conventionally applied.

Thanks.

Cheers,
Wen Shih

frekiwang SG

let (x+1)=y, we have

{y[y(y^0.5)]^0.5}^0.5 [y(y^1.5)^0.5]^0.5=[y(y^0.75)]^0.5=(y^1.75)^0.5=y^0.875

since y^(7/8)=2^(9/2)

y=2^(9/2)^(8/7)=2^(36/7)=35.33

x=y-1=34.33

wee_ws SG

Hi,

frekiwang's method is excellent, via substitution and simple use of indices.

Thanks for sharing!

Cheers,
Wen Shih

eagle SG

Hi,

It is understandably challenging for two reasons:

1. The form is atypical to the student.

2. The method of squaring several times is not conventionally applied.

Thanks.

Cheers,
Wen Shih

Actually I was waiting for the student to think and understand why it was challenging. :)

I was thinking if it was a good method to start asking students on why they think certain questions are challenging and difficult, and not simply brush it off as difficult.

A more challenging question would be unlimited square rooting.

i.e.

Find the value of sqrt (2 sqrt (2 sqrt (2 sqrt (2 sqrt (2 sqrt (2 sqrt (2 sqrt (2 .........))))))))

*Changed question*

wee_ws SG

Hi eagle,

Students I have often encountered find thinking hard because they have no structure provided by schools. The usual comments are 'everything is important', 'just use this/that and problem solved' and 'be self-directed'. :P

Your proposed question can be used as a recurrence question in H2 Maths. I have asked it before in a mock exam I set some years ago :)

Cheers,
Wen Shih

StriveOn SG

Mathematics is like tat one.

When you dunno, it is like Rocket Science.

When you know, you wonder why your friend so stupid.

PhdGuy SG

let (x+1)=y, we have

{y[y(y^0.5)]^0.5}^0.5 [y(y^1.5)^0.5]^0.5=[y(y^0.75)]^0.5=(y^1.75)^0.5=y^0.875

since y^(7/8)=2^(9/2)

y=2^(9/2)^(8/7)=2^(36/7)=35.33

x=y-1=34.33

Once again, I am impressed. Are you a student or tutor?

UltimaOnline SG

Once again, I am impressed. Are you a student or tutor?

frekiwang is an MOE teacher.