(i) Show that (5 + 3v2)² = 43 + 30v2. Hence find, without using a calculator, the positive square root of (ii) 86 + 60v2, giving your answer in the form a+ bv2, where a and b are integers, (iii) 43 – 30V2, giving your answer in the form c+ dV2, where c and d are integers,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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рарer 2
4. INDICES AND SURDS
page 17
2010 N
Q1
(i) Show that (5 + 3v2)² = 43 + 30v2.
Hence find, without using a calculator, the positive square root of
(11) 86 + 60V2, giving your answer in the form a + bv2, where a and b are integers,
(iii) 43 - 30V2, giving your answer in the form c + dV2, where c and d are integers,
1
f+gv2
where f, g and h are integers.
(iv)
43+30V2'
giving
your answer in the form
Transcribed Image Text:рарer 2 4. INDICES AND SURDS page 17 2010 N Q1 (i) Show that (5 + 3v2)² = 43 + 30v2. Hence find, without using a calculator, the positive square root of (11) 86 + 60V2, giving your answer in the form a + bv2, where a and b are integers, (iii) 43 - 30V2, giving your answer in the form c + dV2, where c and d are integers, 1 f+gv2 where f, g and h are integers. (iv) 43+30V2' giving your answer in the form
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