If a−2b=15 and ab=11 then find the value of a2+4b2?

Step 1 (a−2b)2 =a2−4ab+4b2=152 then a2+4b2 152+4ab =152+4×11=269

Step 1 Given that, a−2b=15 ∴(a−2b)2=152=225 ∴a2−2×a×2b+4b2=225 i.e., a2−4ab+4b=225 Letting, ab=11 in this, we have, a2−4(11)+4b2=225 Hence, a2+4b2=225+4269

Step 1 (a−2b)2 =a2−4ab+4b2=152 then a2+4b2 152+4ab =152+4×11=269

Step 1 Given that, a−2b=15 ∴(a−2b)2=152=225 ∴a2−2×a×2b+4b2=225 i.e., a2−4ab+4b=225 Letting, ab=11 in this, we have, a2−4(11)+4b2=225 Hence, a2+4b2=225+4269

Resolved: "If a−2b=15 and ab=11 then find the value..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

m1cadc

Answered question

2022-02-03

a - 2 b = 15

and

a b = 11

then find the value of

a^{2} + 4 b^{2}

Answer & Explanation

Reagan Blair

Beginner2022-02-04Added 16 answers

Step 1

{(a - 2 b)}^{2}

= a^{2} - 4 a b + 4 b^{2} = 15^{2}

then

a^{2} + 4 b^{2}

15^{2} + 4 a b

= 15^{2} + 4 \times 11 = 269

sigcinweq0s

Beginner2022-02-05Added 19 answers

Step 1
Given that,

a - 2 b = 15

∴ {(a - 2 b)}^{2} = 15^{2} = 225

∴ a^{2} - 2 \times a \times 2 b + 4 b^{2} = 225

i.e.,

a^{2} - 4 a b + 4 b = 225

Letting,

a b = 11

in this, we have,

a^{2} - 4 (11) + 4 b^{2} = 225

Hence,

a^{2} + 4 b^{2} = 225 + 4269

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