Grade 10 Maths · Algebra · Evaluate using identities

Evaluate using identities Grade 10

Find the value of expressions like a^2 + b^2 or x^2 + 1x^2 from a given sum and product without solving for the letters, for example (a + b)^2 - 2ab gives a^2 + b^2.

questions use it, all grades · 2 past paper, 17 practice: 19 questions use it, all grades · 2 past paper, 17 practice
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If x+y=5 and xy=6, then find the value of x²+y².USF mathematics world

if x+1/x=3 then find the value of x²+1/x²=?JEETU GUPTA

Most People Get This WRONG: x + 1/x = 3, x² + 1/x² = ?Mia's Math Class

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Question 3.3 · June 2025 · Paper 1 · Provincial · 4 marks

3.3 If

x^{3} + \frac{1}{x ^{3}} = 12

and

x^{2} + \frac{1}{x ^{2}} = 7

.

Determine the value of:

x + \frac{1}{x} + 3

.(4)

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More questions: evaluate using identities

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3. Practice · NavyBlue · 2 marks
If $2 x - 3 y = 5$ and $x y = 2$ , find the value of $4 x^{2} + 9 y^{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Square $(2 x - 3 y)^{2} = 4 x^{2} - 12 x y + 9 y^{2} = 25$
  1 mark · Evaluate using identities
2. ✓
  Answer $4 x^{2} + 9 y^{2} = 25 + 12 (2) = 49$
  1 mark · Evaluate using identities
4. Practice · NavyBlue · 2 marks
If $a^{2} + b^{2} = 34$ and $a + b = 8$ , find the value of $ab$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identity $(a + b)^{2} = a^{2} + b^{2} + 2 ab$
  $64 = 34 + 2 ab$
  1 mark · Evaluate using identities
2. ✓
  Answer $2 ab = 30$
  $ab = 15$
  1 mark · Evaluate using identities
5. Practice · NavyBlue · 2 marks
If $a + b = 7$ and $ab = 10$ , find the value of $a^{2} + b^{2}$ without solving for $a$ and $b$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identity $a^{2} + b^{2} = (a + b)^{2} - 2 ab$
  1 mark · Evaluate using identities
2. ✓
  Answer $7^{2} - 2 (10) = 49 - 20 = 29$
  1 mark · Evaluate using identities
6. Practice · NavyBlue · 2 marks
Given $m - n = 2$ and $m^{2} + n^{2} = 20$ .
(a) Find the value of $mn$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identity $(m - n)^{2} = m^{2} + n^{2} - 2 mn$
  $4 = 20 - 2 mn$
  1 mark · Evaluate using identities
2. ✓
  Answer $mn = 8$
  1 mark · Evaluate using identities

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